Free Printable FP2 Integration

1.

$\frac{f^n\left(x\right)}{n}\ +C$
is the standard result of

a)

$\int_{ }^{ }f^{n-1}\left(x\right)dx$

b)

$\int f'\left(x\right)f^n\left(x\right)dx$

c)

$\int_{ }^{ }f'\left(x\right)f^{n-1}\left(x\right)dx$

d)

$\int f^{n+1}\left(x\right)f'\left(x\right)dx$

2.

$\int\frac{1}{1+x^2}dx\ =$

a)

$\tanh^{-1}x+C$

b)

$\tan^{-1}x+C$

c)

$\tan^{-1}\left(\frac{x}{a}\right)+C$

d)

$\tanh^{-1}\left(\frac{x}{a}\right)+C$

3.

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

a)

$\cosh^{-1}\left(\frac{x}{a}\right)+C$

b)

$\sinh^{-1}\left(\frac{x}{a}\right)+C$

c)

$\cos^{-1}\left(\frac{x}{a}\right)+C$

d)

$\sin^{-1}\left(\frac{x}{a}\right)+C$

4.

$\int\tanh\ x\ dx=$

a)

$\ln\left(\cosh\ x\right)+C$

b)

$\ln\ \left(\sinh\ x\right)+C$

c)

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

d)

$\operatorname{sech}^2x\ +\ C$

5.

$\int\cosh\ x\ \sinh^4x\ dx=$

a)

$\frac{1}{5}\cosh^5x+C$

b)

$\sinh^5x\ +C$

c)

$\frac{1}{5}\sinh^5x+C$

d)

$\cosh^5x+C$

6.

$\int\ \ \frac{1}{\sqrt{x^2+a^2}}dx=$

a)

$\tanh^{-1}\left(\frac{x}{a}\right)+C$

b)

$\sinh^{-1}x+C$

c)

$\cosh^{-1}x\ +C$

d)

$\sinh^{-1}\left(\frac{x}{a}\right)+C$

7.

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

a)

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

b)

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

c)

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

d)

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

8.

$\int\ \cosh^{-1}x\ dx=$

a)

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

b)

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

c)

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

d)

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

9.

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

a)

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

b)

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

c)

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

d)

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

10.

$\int\ \frac{1}{\sqrt{4x^2+12x-40}}dx=$

a)

$\int\ \frac{1}{\sqrt{4\left(x-\frac{3}{2}\right)^2}+49}dx$

b)

$\int\ \ \frac{1}{\sqrt{4\left(x-\frac{3}{2}\right)^2-49}}dx$

c)

$\int\ \frac{1}{2\sqrt{\left(x+\frac{3}{2}\right)^2-49}}dx$

d)

$\int\ \frac{1}{2\sqrt{\left(x+\frac{3}{2}\right)^2-\frac{49}{4}}}dx$

11.

$Solve\ \int_{10}^{20}\ \frac{1}{\sqrt{4x^2+12x-40}}\ dx$

a)

3.22

b)

0.322

c)

32.2

d)

322

12.

$Evaluate\ \ \int_0^2\ \frac{1}{\sqrt{9x^2+4}}dx$

a)

$\frac{1}{3}\ln\ \left(\sqrt{10}-3\right)$

b)

$\frac{1}{3}\sinh^{-1}\left(\frac{1}{3}\right)$

c)

$\frac{1}{3}\ln\ \left(\sqrt{10}+3\right)$

d)

$\frac{1}{3}\cosh^{-1}\left(3\right)$

13.

$Given\ I_n=\int_0^{\frac{\pi}{2}}\ \sin^nx\ dx=\frac{n-1}{n}I_{n-2}.\$

Find $I_4$

a)

$\frac{3}{16}$

b)

$\frac{3}{16}\pi$

c)

$\frac{8}{15}$

d)

$\frac{8}{15}\pi$

14.

$The\ reduction\ formula\ for\ \ \int_0^1\ e^{-x}\left(1-x\right)^n\ dx\ \ \ \ is$

a)

$1+nI_{n-1}$

b)

$1-\frac{n-1}{n}I_{n-1}$

c)

$1-nI_{n-1}$

d)

$1-nI_{n+1}$

15.

$Given\ \ \ I_n=\int_0^{\frac{\pi}{4}}\tan^nx\ dx=\int_0^{\frac{\pi}{4}}\tan^{n-2}x\ \tan^2\ x\ dx.$

Find the reduction formula for $I_n$

a)

$\frac{1}{n-1}-I_{n-2}$

b)

$\frac{1}{n-1}-I_{n-1}$

c)

$\frac{1}{n}-I_{n-2}$

d)

$\frac{n}{n-1}-I_{n-2}$

FP2 Integration

Total questions: 15

Worksheet time: 18mins

Similar Resources on Wayground