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AP Calculus AB: Chapter 9 Practice Test

Mathematics20 CardsCreated 3 months ago

This section provides examples of evaluating a variety of indefinite integrals using basic rules and substitution methods. It includes exponential, polynomial, and trigonometric integrals, as well as guidance on selecting appropriate substitution expressions to simplify integration.

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

2/9u^9/2−2/3u^3/2+C

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Key Terms

Term
Definition

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

2/9u^9/2−2/3u^3/2+C

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

x^5/5+x^2−e^2lnx+C

Evaluate the indefinite integral∫5e^xdx.

5e ^x + C

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

1/2(e^x−e^−x)+C

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

(2x−1)^101/202+C

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

None of the above

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AP Calculus AB: Chapter 9 Practice Test
TermDefinition

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

2/9u^9/2−2/3u^3/2+C

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

x^5/5+x^2−e^2lnx+C

Evaluate the indefinite integral∫5e^xdx.

5e ^x + C

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

1/2(e^x−e^−x)+C

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

(2x−1)^101/202+C

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

None of the above

Evaluate the indefinite integral ∫dx/√x+1

2√x+1+C

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 ?

x^ 4 + 3x^ 2 + 5

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

(7x + 9)

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

1/8e^(2x^4−2)+C

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

6+e^x

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

2√x^4+3x^2+5x−4+C

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

6π

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

12

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

50.5

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

32/3

Evaluate ∫13 7 2 1/x^2√x^2−9 dx

4/819*√10

Evaluate ∫ 2 −2 6 1(/16−x^2)^3/2dx.

1/4*√3

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

4.284

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

0.442