Free Printable Topics 6.9-6.10 AP Review

1.

If f is a continuous function and if $F'\left(x\right)=f\left(x\right)$ for all real numbers x, then $\int_1^3f\left(2x\right)dx=$

a)

$2F\left(3\right)-2F\left(1\right)$

b)

$\frac{1}{2}F\left(3\right)-\frac{1}{2}F\left(1\right)$

c)

$2F\left(6\right)-2F\left(2\right)$

d)

$F\left(6\right)-F\left(2\right)$

e)

$\frac{1}{2}F\left(6\right)-\frac{1}{2}F\left(2\right)$

2.

$\int_{ }^{ }6x\sin\left(x^2\right)dx$

a)

$3x^2\cos\left(x^2\right)+C$

b)

$3\cos\left(x^2\right)+C$

c)

$-3\cos\left(x^2\right)+C$

d)

$6\cos\left(x^2\right)+C$

e)

$-12\cos\left(x^2\right)+C$

3.

$\int_{ }^{ }\frac{1}{4+16x^2}dx$

a)

$\ln\left|4+16x^2\right|+C$

b)

$\frac{1}{32}\ln\left|4+16x^2\right|+C$

c)

$\frac{1}{8}\arctan\left(2x\right)+C$

d)

$\frac{1}{4}\arctan\left(2x\right)+C$

e)

$\frac{1}{4}\arctan\left(4x\right)+C$

4.

$\int_{ }^{ }\frac{dx}{6x+12}$

a)

$6\ln\left|6x+12\right|+C$

b)

$\frac{1}{6}\ln\left|x+2\right|+C$

c)

$\ln\left|x+2\right|+C$

d)

$\ln\left|6x+12\right|+C$

e)

$6\ln\left|x+2\right|+C$

5.

If $w=2x$ , then $\int_0^2f\left(2x\right)dx=$

a)

$\int_0^2f\left(w\right)dw$

b)

$\frac{1}{2}\int_0^2f\left(w\right)dw$

c)

$\frac{1}{2}\int_0^4f\left(w\right)dw$

d)

$\int_0^4f\left(w\right)dw$

e)

$2\int_0^1f\left(w\right)dw$

6.

$\int\frac{1}{\sqrt{4-9x^2}}dx$

a)

$\ln\sqrt{4-9x^2}+C$

b)

$2\sqrt{4-9x^2}+C$

c)

$\arcsin\left(3x\right)+C$

d)

$\frac{1}{3}\arcsin\left(3x\right)+C$

e)

$\frac{1}{3}\arcsin\left(\frac{3x}{2}\right)+C$

7.

$\int_{ }^{ }\left(3\sin^5x\cos x\right)dx$

a)

$\frac{1}{2}\sin^6x+C$

b)

$3\sin^5x+C$

c)

$\frac{1}{2}\sin^5x+C$

d)

$3\cos^6x+C$

8.

$\int_{ }^{ }e^x\sqrt{3-e^x}dx$

a)

$-\frac{2}{3}\left(3-e^x\right)^{\frac{3}{2}}+C$

b)

$\frac{2}{3}\left(3-e^x\right)^{\frac{3}{2}}+C$

c)

$-\left(3-e^x\right)^{\frac{1}{2}}+C$

d)

$\left(3-e^x\right)^{\frac{1}{2}}+C$

9.

$\int_0^{\sqrt{3}}\frac{5}{9+x^2}dx$

a)

$\frac{5\pi}{18}$

b)

$\frac{7\pi}{18}$

c)

$\frac{\pi}{6}$

d)

$\frac{\pi}{3}$

10.

$\int_0^1\left(e^x+3e^{-3x}-e^{-x}\right)dx$

a)

$e-\frac{1}{e^3}+\frac{1}{e}-1$

b)

$e-\frac{1}{e^3}+\frac{1}{e}+1$

c)

$e-\frac{1}{e^3}-\frac{1}{e}-1$

d)

$e+\frac{1}{e^3}-\frac{1}{e}+1$

Topics 6.9-6.10 AP Review

Total questions: 10

Worksheet time: 20mins

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