Chapter 9 Practice Test

Question 1

Evaluate the indefinite integral ∫√u(u^3−1)du.

Answer 1

2/9u^9/2−2/3u^3/2+C

Question 2

Evaluate the indefinite integral∫x^5+2x^2−e^2/x dx.

Answer 2

x^5/5+x^2−e^2lnx+C

Question 3

Evaluate the indefinite integral∫5e^xdx.

Answer 3

5e ^x + C

Question 4

Evaluate the indefinite integral∫e^x+e^−x/2dx.

Answer 4

1/2(e^x−e^−x)+C

Question 5

Evaluate the indefinite integral ∫(2x−1)^100dx

Answer 5

(2x−1)^101/202+C

Question 6

Evaluate the indefinite integral ∫x−1/(x^2−2x+5)^3dx

Answer 6

None of the above

Question 7

Evaluate the indefinite integral ∫dx/√x+1

Answer 7

2√x+1+C

Question 8

Which of the following expression is correct substitution to use for u when evaluating the integral ∫(4x^3+6x)cos(x^4+3x^2+5)dx ?

Answer 8

x^ 4 + 3x^ 2 + 5

Question 9

Which of the following values of u is the correct substitution to use when evaluating the integral ∫sec^2(7x+9)dx ?

Answer 9

(7x + 9)

Question 10

Use the substitution u=(2x^4−2) to evaluate the ∫x^3^e(2x^4−2)dx.

Answer 10

1/8e^(2x^4−2)+C

Question 11

Which of the following values of u is the correct substitution to use when evaluating the integral ∫e^x/6+e^x dx ?

Answer 11

6+e^x

Question 12

Evaluate the integral ∫4x^3+6x+5/√x^4+3x^2+5x−4 dx .

Answer 12

2√x^4+3x^2+5x−4+C

Question 13

What is the area between the curve y = cos x + 3 and the x-axis from x = 0 to x = 2π?

Answer 13

6π

Question 14

What is the area between the curve g (x) = 3x^ 2 + 2 and the x-axis from x = −2 to x = 0?

Answer 14

12

Question 15

What is the area bound by the curve y=x^4−2/x^2 and the x-axis from x=4 to x=6?

Answer 15

50.5

Question 16

What is the area beneath the curve y = −x^ 2 − 6x − 5 and above the x-axis?

Answer 16

32/3

Question 17

Evaluate ∫13 7 2 1/x^2√x^2−9 dx

Answer 17

4/819*√10

Question 18

Evaluate ∫ 2 −2 6 1(/16−x^2)^3/2dx.

Answer 18

1/4*√3

Question 19

Approximate the integral ∫ 4 1 3/x dx using the trapezoidal rule with N=4.

Answer 19

4.284

Question 20

Approximate the integral ∫ 7 1 1/5x dx using the trapezoidal rule with N=3.

Answer 20

0.442