Free Printable Integration techniques

1.

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

a)

x

b)

sin(x)

c)

cos(x)

d)

e^x

2.

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

3.

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

a)

$\ln\left|\sec\left(\theta\right)\ +\ \tan\left(\theta\right)\right|\ +\ C$

b)

$\ln\left|x\ +\ \sqrt{x^2-1}\right|\ +\ C$

c)

$x\sqrt{x^2-1}\ +\ C$

d)

I don't know

4.

$\int\frac{1}{cabin}dcabin$

a)

I don't know

b)

seriously?

c)

a house boat

d)

$\ln\left|cabin\right|\ +\ C$

5.

Integrate $\int_{ }^{ }\sin x\ dx$

a)

$=\tan x+c$

b)

$=-\cos x+c$

c)

$=-\sec x+c$

d)

$=\operatorname{cosec}\ x\ +c$

6.

$\int_{ }^{ }e^{5x}dx\ =$

a)

$e^{5x}+c$

b)

$5e^{5x}+c$

c)

$\frac{1}{5}e^{5x}+c$

d)

none of these

7.

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

a)

$\operatorname{arcsec}\left(x\right)+\ C$

b)

$\ln\left|x\ +\ \sqrt{x^2-1}\right|\ +\ C$

c)

$\ln\left|x\sqrt{x^2-1}\ \right|+\ C$

d)

I don't know

8.

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

a)

$\operatorname{arcsec}\left(x\right)+\ C$

b)

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

c)

$\ln\left|x\sqrt{x^2-1}\ \right|+\ C$

d)

I don't know

9.

Which subsitution would you choose to integrate $\int\sqrt{x^2+1}\ dx$ ?

a)

$x=\sin\theta$

b)

$x=\tan\theta$

c)

$x=\sec\theta$

d)

$x=\cos\theta$

10.

Which subsitution would you choose to integrate $\int\sqrt{1-x^2}\ dx$ ?

a)

$x=\sin\theta$

b)

$x=\tan\theta$

c)

$x=\sec\theta$

d)

$x=\cos\theta$

Integration techniques

Total questions: 10

Worksheet time: 4mins

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