Calculus A Complete Course Canadian 8th Edition Adams – Test Bank

Complete Test Bank With Answers

 

 

Sample Questions Posted Below

 

Chapter 5  Integration

5.1  Sums and Sigma Notation

1) Write sigma notation of 4 – 9 + 16 – 25 +… + .

A) (k + 1)2

B)  k2

C) k2

D) (k + 1)2

E) (k – 1)2

Answer:  B

Diff: 1

2) Evaluate the sum .

A) 420

B) 70

C) 67

D) 417

E) 356

Answer:  A

Diff: 1

3) Evaluate . 

A) 1 + 

B) 

C) – 

D) 1 – 

E) – 

Answer:  C

Diff: 1

4) Evaluate the .

A)  + 

B)  – 

C) 

D) 2 – 

E) 2 + 

Answer:  A

Diff: 1

5) Find and evaluate the sum .

A) 

B) – 

C) 

D) – 

E) 

Answer:  B

Diff: 2

6) Evaluate .

A) -1

B) 0

C) 51

D) 1

E) 101

Answer:  D

Diff: 2

7) Express the sum   +  +  +  +…..  +    using sigma notation.

A) 

B) 

C) 

D) 

E) 

Answer:  A

Diff: 2

8) Simplify the expression .

A) ln((2n)!)

B) 

C) (2 ln n)!

D) 2 ln(n!)

E) (ln(n))!

Answer:  D

Diff: 2

9) Express the sum in the series .

A) 2k3 + 9k2 + 7k

B) 2k3 + 9k2 + 5k

C) 3k3 + 9k2 + 7k

D) 3k3 + 9k2 + 5k

E) 2k3 – 9k2 + 7k

Answer:  A

Diff: 3

10) Evaluate the sum   Hint:   =  – .

A) 1

B) 

C) 

D) 

E) 

Answer:  C

Diff: 3

11) Evaluate the sum  .

A) 

B) 

C) 

D) 

E) 

Answer:  D

Diff: 3

12) Express the sum  as a polynomial function of n.

A) 3n3  +  n2 +  n

B) 3n3 +  n2 –  n

C) 3n3 +  n2 + 4n

D) 3n3 + 3 n2 –  n

E) 3n3 –  n2 –  n

Answer:  E

Diff: 1

5.2  Areas as Limits of Sums

1) Find an approximation for the area under the curve  y = 1 –   and above the x-axis from  x =  0  to  

x = 1  using a sum of areas of four  rectangles each having width  1/4  and  (a) tops lying under the curve,  or  (b) tops lying above the curve.  What does this tell you about the actual area under the curve? 

A) (a)  ,   (b)   ;     <  area under curve  <  

B) (a)  ,   (b)   ;     <  area under curve  <  

C) (a)  ,   (b)   ;     <  area under curve  <  

D) (a)  ,   (b)   ;     <  area under curve  <  

E) (a)  ,   (b)   ;     <  area under curve  <  

Answer:  A

Diff: 1

2) Given that the area under the curve  y = x2  and above the x-axis from  x = 0  to  x = a > 0  is   square units, find the area under the same curve from  x = -2  to  x = 3. 

A)   square units

B)   square units

C) 9  square units

D) 6  square units

E) 

Answer:  A

Diff: 2

3) Construct  and simplify a sum approximating the area above the x-axis and under the curve  y = x2  between x = 0  and  x = 3  by using  n  rectangles having equal widths  and tops lying under or on the curve.  Find the actual area as a suitable limit. 

A) ,  area = 9 square units 

B) ,  area = 9 square units

C) ,  area = 6 square units

D) ,  area = 6 square units

E) ,  area = 9 square units

Answer:  A

Diff: 1

4) Construct and simplify a sum approximating the area above the x-axis and under the curve  y = x2  between x = 0  and  x = 3  by using  n  rectangles having equal widths  and tops lying above or on the curve.  Find the actual area as a suitable limit. 

A) ,  area = 9 square units 

B) ,  area = 9 square units  

C) ,  area = 6 square units 

D) ,  area = 6 square units 

E) ,  area = 9 square units

Answer:  A

Diff: 1

5) Write the area under the curve  y = cos x  and above the interval  [0, π/2]  on the x-axis as the limit of a sum of areas of  n  rectangles of equal widths.  Have the upper-right corners of the rectangles lie on the curve. 

A) Area =   

B) Area =  

C) Area =  

D) Area =  

E) Area =   

Answer:  A

Diff: 2

6) Given that =  ,  find the area under  y = x3  and above the interval  [0, a]  on the x-axis  (where  a > 0 )  by interpreting the area as a limit of a suitable sum. 

A)   square units 

B)   square units

C)   square units

D)   square units

E)   square units

Answer:  A

Diff: 2

7) The limit   represents the area of a certain region in the xy-plane. Describe the region. 

A) region under  y = cos x,  above  y = 0,  between x = 0  and  x = 

B) region under  y = sin x,  above  y = 0,  between x = 0  and  x = 

C) region under  y = cos x,  above  y = 0,  between x = 0  and  x = π

D) region under  y = sin x,  above  y = 0,  between x = 0  and  x = π

E) region under  y = cos x,  above  y = 0,  between x=  and  x = π

Answer:  D

Diff: 2

8) By interpreting it as the area of a region in the xy-plane, evaluate the limit

 .

A) 2 + 2π  (the area of the trapezoidal region under  y = 1 + πx,  above  y = 0  from  x = 0  to  x = 2)

B) 1 + π  (the area of the trapezoidal region under  y = 1 + 2πx,  above  y = 0  from  x = 0  to  x = 1)

C) 2 + 4π  (the area of the trapezoidal region under  y = 1 + 2πx,  above  y = 0  from  x = 0  to  x = 2)

D) 4 + 2π  (the area of the trapezoidal region under  y = 2 + πx,  above  y = 0  from  x = 0  to  x = 2)

E) 2  +   (the area of the trapezoidal region under  y = 2 + πx,  above  y = 0  from  x = 0  to  x = 1)

Answer:  A

Diff: 2

9) By interpreting it as the area of a region in the xy-plane, evaluate the limit

 .

A) π  (the area of a quarter of a circular disk of radius 2)

B) 2π  (the area of half of a circular disk of radius 2)

C) 4π  (the area of a circular disk of radius 2)

D) 8π  (the area of half of a circular disk of radius 4)

E) 16π  (the area of a circular disk of radius 4)

Answer:  A

Diff: 2

5.3  The Definite Integral

1) Let  P denote the partition of the interval  [1, 3]  into 4 subintervals of equal length Δx = 1/2.  

Evaluate the upper and lower Riemann sums  U(f, P)  and  L(f,P) for the function  f(x) = 4 x2.

A) U(f,P) = 40,  L(f,P) = 30 

B) U(f,P) = 41,  L(f,P) = 29 

C) U(f,P) = 42,  L(f,P) = 28 

D) U(f,P) = 43,  L(f,P) = 27 

E) U(f,P) = 44,  L(f,P) = 26

Answer:  D

Diff: 1

2) Let  P denote the partition of the interval  [1, 2]  into 8 subintervals of equal length Δx = 1/8.  

Evaluate the upper and lower Riemann sums  U(f, P)  and  L(f,P) for the function  f(x) = 1/x. 

Round your answers to 4 decimal places.

A) U(f,P) = 0.7110,  L(f,P) = 0.6781

B) U(f,P) = 0.7254,  L(f,P) = 0.6629

C) U(f,P) = 0.7302,  L(f,P) = 0.6571

D) U(f,P) = 0.7378,  L(f,P) = 0.6510

E) U(f,P) = 0.7219,  L(f,P) = 0.6683

Answer:  B

Diff: 1

3) Let  P denote the partition of the interval  [1, 4]  into 6 subintervals of equal length Δx = 1/2.  

Evaluate the upper and lower Riemann sums  U(f, P)  and  L(f,P) for the function  f(x) = . 

Round your answers to 4 decimal places. 

A) U(f,P) = 4.9115,  L(f,P) = 4.4115

B) U(f,P) = 4.9135,  L(f,P) = 4.4109

C) U(f,P) = 4.9180,  L(f,P) = 4.4057

D) U(f,P) = 4.9002,  L(f,P) = 4.4250

E) U(f,P) = 4.9183,  L(f,P) = 4.4093

Answer:  A

Diff: 1

4) Calculate the upper Riemann sum for  f(x) = x2 + 1  corresponding to a partition  P  of the interval  [0, 3]  into n equal subintervals of length 3/n.  Express the sum in closed form and use it to calculate the area under the graph of  f,  above the x-axis,  from  x = 0  to  x = 3. 

A) U(f,P) =  + 3,  area = 12 square units

B) U(f,P) =  + 3,  area = 12 square units

C) U(f,P) =  + 3,  area = 12 square units 

D) U(f,P) =  + 3,  area = 12 square units

E) U(f,P) =  + 3,  area = 12 square units

Answer:  C

Diff: 1

5) Calculate the lower Riemann sum for  f(x) = ex corresponding to a partition  P  of the interval  [0, 1]  into n equal subintervals of length  1/n.  Given that n  = 1  (which can be verified by using l’Hopital’s Rule),  find the area under y = ex and above the x-axis between  x = 0  and  x = 1.

A) L(f,P) = ,  area = e  square units

B) L(f,P) = ,  area =   square units

C) L(f,P) = ,  area = e – 1  square units

D) L(f,P) = ,  area =   square units

E) L(f,P) = ,  area =   square units

Answer:  C

Diff: 2

6) Express  dx  as a limit of Riemann sums corresponding to partitions of  [0, 1]  into equal subintervals and using the values of  f  at the midpoints of the subintervals.

A) dx  =   

B) dx  =  

C) dx  =  

D) dx  =  

E) dx  =   

Answer:  E

Diff: 2

7) Express  dx  as a limit of lower Riemann sums corresponding to partitions of  [0, 2]  into equal subintervals. 

A) dx  =  . 

B) dx  =  . 

C)  dx  =  . 

D) dx  =  . 

E) dx  =  . 

Answer:  A

Diff: 2

8) Write the following limit as a definite integral: 

. 

A)  

B) 

C) 

D) 

E) 

Answer:  A

Diff: 2

9) Write the following limit as a definite integral:

 

A)  

B) 

C) 

D) 

E) 

Answer:  A

Diff: 2

10) Use the limit definition of definite integral to evaluate dx.

A) 0

B) – 

C) 

D) 1

E) -1

Answer:  A

Diff: 2

11) Use the limit definition of the definite integral to evaluate dx.

A) 10

B) 18

C) 6

D) 30

E) 9

Answer:  D

Diff: 2

12) Write the following limit as a definite integral:

A) dx

B) dx

C) dx

D) dx

E) dx

Answer:  A

Diff: 3

5.4  Properties of the Definite Integral

1) Given that  and  = -1,  find 

A) -3

B) -1

C) 3

D) 1

E) -2

Answer:  A

Diff: 1

2) Suppose that 

A) -5

B) -3

C) -7

D) -1

E) 7

Answer:  C

Diff: 2

3) Evaluate dx.

A) 42

B) 0

C) 21

D) 51

E) 16

Answer:  A

Diff: 1

4) True or False:   If f and g are integrable functions on the interval [a, b], then

= . dx.

Answer:  FALSE

Diff: 1

5) Evaluate  dx.

A) 0

B) 1

C) -1

D) 

E) – 

Answer:  B

Diff: 2

6) True or False:  If  f(x) is an even function and g(x) is an odd function over the same interval [-a, a], then

 

Answer:  TRUE

Diff: 1

7) Evaluate (2 – ) dx  by interpreting the integral as representing an area. 

A) 

B) 4

C) 2

D) 

E) – 

Answer:  A

Diff: 1

8) Evaluate  dx  by interpreting the integral as representing an area. 

A) 8π

B) 4π

C) 16π

D) 8

E) 16

Answer:  A

Diff: 1

9) Given that   dx = ,  evaluate   dx.

A) π/4

B) π/2

C) π

D) 1/2

E) 

Answer:  A

Diff: 1

10) Given the piecewise continuous function  f(x) = 

evaluate  by using the properties of definite integrals and interpreting integrals as areas.

Answer:   8

Diff: 2

11) Find the average value of the function  f(x) = 3 + 4x  on  [0, 2].

A) 7

B) 6

C) 8

D) 3

E) 9

Answer:  A

Diff: 1

12) Find the average value of the function  f(x) = sin (x/2) + π  on  [-π, π].

A) π

B) 

C) 2π

D) 

E) 2

Answer:  A

Diff: 1

13) What is the average value of  f(x) =   on the interval  [0, 2]?

A) 

B) 

C) π

D) 

E) 2π

Answer:  A

Diff: 1

14) What values of a and b, satisfying  a < b,  maximize the value of 

A) a = 0, b = 1

B) a = -1, b = 1

C) a = 0, b = 2

D) a = -∞, b = ∞

E) a = -1, b = 0

Answer:  A

Diff: 3

15)  What values of a and b, satisfying  a < b,  maximize the value of 

A) a = -2,  b = 4

B) a = 0,  b = 4

C) a = -∞,  b = ∞

D) a = -2,  b = 0

E) a = 1,  b = 3

Answer:  A

Diff: 3

5.5  The Fundamental Theorem of Calculus

1) Evaluate the definite integral 

A) – 

B) 

C) 

D) – 

E) -12

Answer:  B

Diff: 1

2) Compute the definite integral – 2x + 1)dx.

A) 14

B) 22

C) 21

D) 24

E) 20

Answer:  D

Diff: 1

3) Compute the integral – x)dx.

A) 4 – 

B) 4 + 

C) 4 – 

D) 4  + 

E) 2  – 

Answer:  A

Diff: 2

4) Compute the integral 

A) 

B) 

C) – 

D) – 

E) 

Answer:  B

Diff: 2

5) Evaluate the integral dx.

A) 

B) 1

C) 

D) 

E) 

Answer:  A

Diff: 2

6) Find dx.

A)  

B) 

C) 

D) 

E) 

Answer:  D

Diff: 2

7) Evaluate the integral 

A) 

B) 

C) 

D) 

E) – 

Answer:  C

Diff: 2

8) Find the average value of the function f(x) = x4 + 3×3 – 2×2 – 3x + 1 on the interval [0, 2].

A) 

B) 

C) 

D) 

E) 

Answer:  A

Diff: 2

9) Find the average value of the function f(x) = sin x on [0, 3π/2].

A) 

B) 

C) 

D) 

E) 

Answer:  B

Diff: 2

10) Evaluate the definite integral dx.

A) 11.1

B) 9.9

C) 10.1

D) 15

E) -10.1

Answer:  C

Diff: 2

11) Evaluate the integral dx.

A) 4

B) 6

C) 7

D) 5

E) 3

Answer:  D

Diff: 2

12) Evaluate the integral 

A) 1

B) 0

C) -1

D) -2

E) 2

Answer:  A

Diff: 1

13) Find the average value of the function f(x) = sec2 3x,over the interval [-π/12, π/12].

A) 

B) 

C) 

D) 

E) 

Answer:  C

Diff: 2

14) Let  f(t) = 

Evaluate  dt.

Answer:   

dt.= 

Diff: 3

15) Evaluate the definite integral dx.

A) – 

B) 

C) 

D) -33

E) 

Answer:  C

Diff: 2

16) Find the derivative of  F(x) =

A) 2 ln x

B) 0

C) -ln xn x

D)  ln x

E)  ln x

Answer:  D

Diff: 2

17) Find the derivative of F(x) = dt.

A) 2e2x cos (e4x)

B) 2e2x sin (e4x)

C) 2e2x cos (e2x)

D) e2x  cos (e4x)

E) ex cos (e4x)

Answer:  A

Diff: 2

18) Given that the relation  3×2 + dt = 3  defines y implicitly as a differentiable function of x, find .

A) 

B) 

C) 6x + cos (t) – t sin (t)

D) 6x +cos(y) – ysin (y)

E) 6x + ycos (y)

Answer:  A

Diff: 3

19) Evaluate 

A) – 

B) – 

C) 

D) 1

E)  

Answer:  B

Diff: 3

20) Find the point on the graph of the function  f(x) = dt  where the graph has a horizontal tangent line.

A) 

B) 

C) 

D) (1, 0)

E) 

Answer:  A

Diff: 3

21) True or False: Since the derivative of –  is , the Fundamental Theorem of Calculus implies that 

dx = –  +  = -2.  

Answer:  FALSE

Diff: 3

5.6  The Method of Substitution

1) Evaluate the integral  dx.

A)  (6 + x)16  +  C

B)  (6 + x)15  +  C

C)  (6 + x)16  +  C

D) –  (6 + x)16  +  C

E) –  (6 + x)16  +  C

Answer:  A

Diff: 1

2) Find the inflection point of the function f(x) = dt, where x > 0.

A) (1, 0)

B) (e, )

C) (e,  1)

D) (e, )

E) 

Answer:  D

Diff: 3

3) Evaluate the integral dx.

A) ln(3) + C

B) ln  + C

C) 3ln  + C

D)  + C

E)  + C

Answer:  C

Diff: 1

4) Evaluate the integral  dx.

A) e(x2 + 2x + 3) + C

B) e(x2 + 2x + 3) + C

C) – e (x2 + 2x + 3) + C

D) – e(x2 + 2x + 1) + C

E) 2 e(x2 + 2x + 3) + C

Answer:  A

Diff: 1

5) Evaluate the integral 

A)  – 

B)  + 

C)  – 

D)  + 

E) 

Answer:  D

Diff: 2

6) Evaluate the integral  dx.

A)  + C

B)  + C

C)  + C

D)  + C

E)  + C

Answer:  C

Diff: 2

7) Evaluate the integral dx.

A)  ln(x2 + 4x + 5) + C

B) 2 ln(x2 + 4x + 5) + C

C)  ln(x2 + 4x + 5) + C

D) -2  ln(x2 + 4x + 5) + C

E) –  ln(x2 + 4x + 5) + C

Answer:  C

Diff: 2

8) Evaluate the integral dx.

A)   + C

B)   + C

C)   + C

D)   + C

E)   + C

Answer:  B

Diff: 2

9) Evaluate the integral  dx.

A)  + C

B)  + C

C)  + C

D)  + C

E)  + C

Answer:  D

Diff: 2

10) Evaluate the integral dx.

A)   + C

B) -3  + C

C)   + C

D) –   + C

E) –   + C

Answer:  A

Diff: 2

11) Evaluate the integral cos (e2x) dx.

A)  + C

B)  + C

C) –  + C

D) –  + C

E)  + C

Answer:  B

Diff: 2

12) Evaluate dx.

A) 1

B) 0

C) 2

D) 

E) π

Answer:  A

Diff: 2

13) Evaluate (3x) (3x) dx.

A)  sin(3x)  + C  

B)  sin(3x)  + C  

C)  sin(3x)  + C  

D)  sin(3x)  + C  

E)  sin(3x)  + C  

Answer:  A

Diff: 2

14) Evaluate (πx) dx.

A) 

B) 

C) 1

D) 

E) π

Answer:  A

Diff: 2

15) Evaluate x  x dx.

A) 

B) 

C) 

D) 

E) π

Answer:  A

Diff: 2

16) Evaluate x dx.

A)  – 

B)  + 

C) 

D) 

E)  – 

Answer:  A

Diff: 2

17) Evaluate .

A)  

B)  

C) π

D) 1

E) 

Answer:  A

Diff: 2

18) Evaluate sinh(x) dx

A) 2 ex cosh(x) + C

B)  –  + C

C) e2x – x + C

D) 2 ex cosh(x) – 2ex sinh(x) + C

E)  e2x + x + C

Answer:  C

Diff: 2

19) Evaluate the integral 

A)   +  + C

B)   +  + C

C)   +  + C

D)   +  + C

E)   –  + C

Answer:  D

Diff: 2

20) Evaluate the integral dx.

A)   + C

B) –  + C

C)   + C

D) –  + C

E)  + C

Answer:  D

Diff: 3

21) Evaluate the integral dx.

A) –   + C

B)    + C

C) –   + C

D)    + C

E) –   + C

Answer:  A

Diff: 2

22) Evaluate the integral dx.

A)  + C 

B)  + C 

C)  ln + C

D)  ln + C

E) ln + C

Answer:  D

Diff: 2

23) Evaluate the integral dx.

A)  tan-1 + C

B)  tan-1 + C

C)  tan-1 + C

D)  tan-1 + C

E)  tan-1 + C

Answer:  C

Diff: 2

24) Evaluate  dx.

A) 2 ln + C

B)  + ln + C

C) ln + C

D) 

E)  + C

Answer:  C

Diff: 2

25) True or False:  dx = –  + C

Answer:  TRUE

Diff: 2

26) Evaluate the integral dx.

A)  + C

B)  + C

C)  + C

D)  + C

E) 2 + C

Answer:  A

Diff: 3

27) Evaluate the integral dx.

A)  –  + C

B)  –  + C

C)  –  + C

D)  +  + C

E)  –  + C

Answer:  B

Diff: 3

28) Evaluate the integral dx.

A) tan-1(et) + C

B) tan-1(e2t) + C

C) tan-1(et) + C

D) tan-1(e2t) + C

E) tan-1(e4t) + C

Answer:  B

Diff: 3

29) Evaluate the integral dx.

A)  + C

B)  + C

C)  + C

D)  + C

E) 2 + C

Answer:  D

Diff: 3

5.7  Areas of Plane Regions

1) Find the area of the finite plane  region bounded by the graphs of the equations y = x4 and y = 4.

A)   square units 

B)   square units 

C)   square units 

D)   square units

E) 1  square unit

Answer:  B

Diff: 1

2) Find the area of the finite plane region bounded by the graphs of the equations y = x3, y = 0, x = 1, and
x = 3.

A) 10 square units 

B) 15 square units 

C) 20 square units 

D) 25 square units 

E) 30 square units

Answer:  C

Diff: 1

3) Find the area of the finite plane region bounded by the graphs of the equations y = ,  ,
x = 4.

A)   square units 

B)   square units 

C)   square units 

D) 11 square units 

E)   square units

Answer:  C

Diff: 1

4) Find the area of the finite region bounded by the graphs of the equations y = x2 – 4  and  y = 4 – x2.

A) 16  square units 

B) 22  square units 

C)   square units 

D)   square units 

E)   square units

Answer:  D

Diff: 2

5) Find the area of the region lying in the first quadrant above the curve  xy = 4 and below the line 
x + y = 5.

Answer:   – 8 ln(2) square units

Diff: 2

6) Find the area of the region lying in the first quadrant above the curve  xy = 4 and below the line 
x + y = 5.

A)  + 4 ln(5) square units

B)  – 8 ln(2) square units

C)  – 8 ln(2) square units

D)  + 8 ln(2) square units

E)  – 4 ln(5) square units

Answer:  B

Diff: 2

7) Find the area of the finite plane region bounded by the graphs of the equations y = x5,  x = 0, and
y = 81.

A)   square units

B) 334  square units

C)   square units

D) 203  square units

E)   square units

Answer:  E

Diff: 2

8) Find the area of the finite region bounded by the graphs of the functions  f(x) = x2 and  g(x) = x3.

A)   square units

B)   square units

C)   square units

D)   square units

E)   square units

Answer:  E

Diff: 1

9) Find the area of the region enclosed by the graphs of  y = ex  and  y = 1 – 2x  from x = 0 to x = 1.

A) e – 1  square units

B) e + 1  square units

C) e  square units

D) 1 – e  square units

E) 1  square unit

Answer:  A

Diff: 1

10) Find the area of the region enclosed by the curves y = cosh(x), y = – sinh(x), and 0 ≤ x ≤ ln(4) (shown in the figure below).

Answer:  area = 3 square units

Diff: 2

11) Find the area of the region bounded by the graphs of the equations x = y2 – 2 and y = -x.

A)   square units

B)   square units

C) 3 square units

D)   square units

E)   square units

Answer:  D

Diff: 2

12) Find the area of the finite region in the first quadrant bounded by the graphs of the equations 3y2 = x3  and  y2 = 3x.

A)   square units

B)   square units

C)   square units

D)   square units

E)   square units

Answer:  C

Diff: 2

13) Find the area of the finite plane region bounded by the graphs of the equations y = cot x, y = 0, , and .

A)  ln 2 square units

B)  ln 2 square units

C) ln 2 square units

D)  ln 2 square units

E) 2 ln 2 square units

Answer:  B

Diff: 2

14) Find the area of the first quadrant region lying under the curve  +   = , where a > 0. 

A)    square units

B)   square units

C)   square units

D)   square units

E)  square units

Answer:  D

Diff: 2

15) Find the area of the region lying between the graphs of the equations y = sin x and y = cos x from 0 to 2π.

A) 2 square units

B) 4 square units

C) 6 square units

D) 3 square units

E)  square units

Answer:  B

Diff: 3

16) Find the area inside the circle x2 + y2 = a2 and outside the ellipse b2 x2 + a2 y2 = a2 b2,  here a > b. 

A) πa  square units

B)   square units

C) 2πa  square units

D)   square units

E) πb(a – b)  square units

Answer:  A

Diff: 3

17) Find the constant real number m such that the line y = mx bisects the area of the finite plane region enclosed by the curve y = 2x – x2 and the x-axis. Refer to the figure below.

Answer:  m = 2 – ≈ 0.413

Diff: 2

18) Find the area of the region bounded by the graphs of the equations y2 = 2px  and x2 = 2py ,
where p > 0.

A) p3 square units

B) p2 square units

C) p2 square units

D) p2 square units

E) 2p2 square units

Answer:  C

Diff: 3

19) Find the total area of the two finite plane regions bounded by the curves x2 + y = 4  and  x2 y = 3.

A) 8 –   square units

B) 8 –   square units

C) 8 –   square units

D) 8 –   square units

E) 8 – 14 square units

Answer:  C

Diff: 3

Calculus: A Complete Course, 8e

Chapter 5: Integration

Copyright © 2014 Pearson Canada Inc., Toronto, Ontario5- PAGE   \* MERGEFORMAT 38