Free Printable 12A-T3

1.

What would you choose for your u here if you used integration by parts?

a)

ln x

b)

ln (x) sin (x)

c)

sin (x)

d)

x

2.

What would you choose for your u here if you used integration by parts?

a)

t

b)

3t

c)

e^2t

d)

e^t

e)

don't use IBP, let u = 2t

3.

What method would you use here?

a)

antiderivatives

b)

u-substitution

c)

integration by parts

d)

slope fields

4.

What method would you use here?

a)

antiderivatives

b)

u-substitution

c)

integration by parts

d)

slope fields

5.

This can be integrated using u-substitution. What should "u" equal in this integral?

a)

x

b)

(lnx)/x

c)

lnx

d)

sin(lnx)

6.

U-substitution works for this integral. What should be assigned to u in the integral?

a)

2x²

b)

4x

c)

5x

d)

no u needed

7.

Which technique should be used to integrate this:

a)

antiderivatives

b)

u-substitution

c)

integration by parts

d)

partial fraction

8.

Which technique would you use to integrate this:

a)

antiderivatives

b)

u-substitution

c)

integration by parts

d)

partial fraction

9.

Integrate $\int7x^6\left(x^7+1\right)^8dx$

a)

$\frac{\left(x^7-1\right)^9}{9}+c$

b)

$\frac{\left(x^7+1\right)^9}{9}+c$

c)

$\frac{\left(x^7+1\right)^8}{8}+c$

d)

$\frac{\left(7x^6+1\right)^9}{9}+c$

10.

Find the indefinite integral.

a)

¹/₂x² - 8 ln x + C

b)

x² - 8 + C

c)

2x² - 8 ln x + C

d)

¹/₂x² - 8x + C

e)

x² - ln x + C

11.

Change this form $\int x\sqrt{x^2+1\ }dx$ into

a)

$x\left(x^2+1\right)^{\frac{1}{2}}$

b)

$\int x\left(x^2+1\right)^{\frac{1}{2}}dx$

c)

$\int x\left(2x+1\right)^{\frac{1}{2}}dx$

d)

$\int\left(x^2+1\right)^{\frac{1}{2}}dx$

12.

Integrate $\int\frac{2x}{\sqrt{3+x^2}}dx$ using substitution methods

a)

$\frac{1}{2\left(3+x^2\right)^{\frac{1}{2}}}+c$

b)

$\left(3+2x\right)^{\frac{1}{2}}+c$

c)

$2\left(3+x^2\right)^{\frac{1}{2}}+c$

d)

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

13.

What should "du" equal in this integral?

a)

tanxsecx dx

b)

secx dx

c)

sec²x dx

d)

tanx dx

14.

Given $\frac{\text{d}}{\text{d}x}\ln\left(\cos x\right)=-\frac{\sin x}{\cos x}=-\tan x$ , $\int_{ }^{ }\tan xdx=$

a)

$\ln\left(\cos x\right)+c$

b)

$-\ln\left(\cos x\right)+c$

c)

$\sec^2x+c$

d)

$-\sec^2x+c$

15.

What should be used for u in the integral?

a)

no u needed

b)

4t²

c)

t³

d)

1/4t²

12A-T3

Total questions: 15

Worksheet time: 14mins

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