Chapter 9 Test

Question 1

Evaluate the indefinite integral ∫(2x^4+√3x+1)dx.

Answer 1

2/5 x^5+2√3/3 x^3/2+x+C

Question 2

Evaluate the indefinite integral∫x^3+3x^2−ln3/√x dx

Answer 2

2/7 x^7/2+6/5 x^5/2−(2ln3)x^1/2+C

Question 3

Evaluate the indefinite integral∫⎛⎝e^x/5+x^2√x⎞⎠dx.

Answer 3

e^x/5+2/7x^7/2+C

Question 4

Evaluate the indefinite integral∫sin x/cos√2dx.

Answer 4

−cos x/cos√2+C

Question 5

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

Answer 5

-1/5(5x-3) + C

Question 6

Evaluate the indefinite integral ∫dx/√x(1−√x)^3

Answer 6

1/(1−√x)^2+C

Question 7

Evaluate the indefinite integral ∫x^2dx/x^3−e^3

Answer 7

1/3ln∣x^3−e^3∣+C

Question 8

Use the substitution u=(x^4+3x^2+5)to evaluate the integral∫(4x^3+6x)cos(x^4+3x^2+5)dx.

Answer 8

sin (x ^4 + 3x ^2 + 5) + C

Question 9

Use the substitution u=(7x+9) to evaluate the integral ∫sec^2(7x+9)dx .

Answer 9

1/7tan(7x+9)+C

Question 10

Which of the following values of u is the correct substitution to use when evaluating the integral ∫x^3e^(2x^4−2)dx ?

Answer 10

(2x^ 4 − 2)

Question 11

Use the substitution u=6+e^x to evaluate the integral∫e^x/6+e^x dx .

Answer 11

ln|6+e^x|+C

Question 12

Evaluate ∫(12x^3−18x−27)e^(x^4−3x^2−9x+1)dx.

Answer 12

3e^(x^4−3x^2−9x+1)+C

Question 13

What is the area beneath the curve y = e^ 3x + 3 from x = −1 to x = 4?

Answer 13

1/3(e^15−1)

Question 14

What is the area beneath the curve y = x^1/2+1/x from x = 4 to x = 9?

Answer 14

38/3+ln9/4

Question 15

What is the area between the curve h(x)=sin x+cos x and the x-axis from x= 0 to x = π/2?

Answer 15

2

Question 16

What is the area beneath the curve g (x) = e^ x + 2x + cos x from x = π to x = 2π?

Answer 16

e^2π−e^π+3π^2

Question 17

Evaluate ∫ 2 -1 5 1/(9−x^2)^3/2dx.

Answer 17

2/9 √5+5/36 √2

Question 18

Evaluate ∫3 −1 7 x/√36−x^2 dx.

Answer 18

−21√3+7√35

Question 19

Approximate the integral ∫ 6 2 x^2 dx using the trapezoidal rule N=4.

Answer 19

70

Question 20

Approximate this integral ∫π/2 π/4 sin(x) dx using the trapezoidal rule with N=4.

Answer 20

0.705