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AP Calculus AB: Chapter 9 Test

Mathematics20 CardsCreated 8 months ago

This section contains a series of indefinite integral problems solved using standard integration rules, substitution, and simplification techniques. It features exponential, logarithmic, trigonometric, and rational expressions, demonstrating the diversity of integration strategies required across different function types.

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

2/5 x^5+2√3/3 x^3/2+x+C

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Key Terms

Term
Definition

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

2/5 x^5+2√3/3 x^3/2+x+C

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

2/7 x^7/2+6/5 x^5/2−(2ln3)x^1/2+C

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

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

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

−cos x/cos√2+C

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

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

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

1/(1−√x)^2+C

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AP Calculus AB: Chapter 9 Test
TermDefinition

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

2/5 x^5+2√3/3 x^3/2+x+C

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

2/7 x^7/2+6/5 x^5/2−(2ln3)x^1/2+C

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

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

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

−cos x/cos√2+C

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

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

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

1/(1−√x)^2+C

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

1/3ln∣x^3−e^3∣+C

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

sin (x ^4 + 3x ^2 + 5) + C

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

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

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

(2x^ 4 − 2)

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

ln|6+e^x|+C

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

3e^(x^4−3x^2−9x+1)+C

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

1/3(e^15−1)

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

38/3+ln9/4

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

2

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

e^2π−e^π+3π^2

Evaluate ∫ 2 -1 5 1/(9−x^2)^3/2dx.

2/9 √5+5/36 √2

Evaluate ∫3 −1 7 x/√36−x^2 dx.

−21√3+7√35

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

70

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

0.705