Free Printable TEST 2

1.

Find the Integrals of $\frac{x+2}{2x^{2\ }+6x+5}$

a)

$\frac{1}{4}\log\left|2x^{2\ }+6x+5\right|+\frac{1}{2}\tan^{-1}\left(2x+3\right)+c_1$

b)

$\frac{1}{4}\log\left|2x^{2\ }+6x+5\right|+\frac{1}{2}\log\left(\frac{x+2}{x+1}\right)+c_1$

c)

$\frac{1}{4}\log\left|2x^{2\ }+6x+5\right|+\frac{1}{2}\log\left|\frac{x+1}{x+2}\right|+C$

d)

$\frac{1}{4}\log\left|2x^{2\ }+6x+5\right|+\frac{1}{2}\tan^{-1}\ \frac{x+\frac{3}{2}}{\frac{1}{2}}+c$

2.

Find Integral of $\sqrt[2]{x^{2\ }-8x+7}$ is equal to

a)

$\frac{\left(x-4\right)}{2}\sqrt{\ x^{2\ }-8x+7}+9\ \log\left|x-4+\sqrt{\ x^{2\ }-8x+7}\right|+C$

b)

$\frac{\left(x+4\right)}{2}\sqrt{\ x^{2\ }-8x+7}+9\ \log\left|x+4+\sqrt{\ x^{2\ }-8x+7}\right|+C$

c)

$\frac{\left(x-4\right)}{2}\sqrt{\ x^{2\ }-8x+7}+3\sqrt{\ 2}\ \log\left|x-4+\sqrt{\ x^{2\ }-8x+7}\right|+C$

d)

$\frac{\left(x-4\right)}{2}\sqrt{\ x^{2\ }-8x+7}-\frac{9}{2}\ \log\left|x-4+\sqrt{\ x^{2\ }-8x+7}\right|+C$

3.

$\int6x\left(3x^2+5\right)^{5\ }dx\ =\ ...$

a)

$\frac{1}{3}\left(3x^2+5\right)^5+\ c$

b)

$\frac{2}{3}\left(3x^2+5\right)^{5\ }+\ c$

c)

$\frac{1}{6}\left(3x^2+5\right)^6+\ c$

d)

$\frac{1}{3}\left(3x^2+5\right)^6+\ c$

e)

$\frac{2}{3}\left(3x^2+5\right)^6+\ c$

4.

If $f'\left(x\right)=\ 3x^2-6x+2\$ and $f\left(1\right)=4,\$ Find $f\left(x\right)\$

a)

$x^3-3x^2+3x+4$

b)

$x^3-3x^2+2x+4$

c)

$x^3-3x^2+x+4$

d)

$x^3-3x^2+2x-4$

e)

$x^3-3x^2+3x-7$

5.

Determine $\int_2^3\ \left(6x^2-2x+7\right)\ dx\$

a)

32

b)

34

c)

36

d)

38

e)

40

6.

$\int_{ }^{ }\sqrt{x^5}\ dx\ =\ ...$

a)

$\frac{2}{7}x^{3\ }\sqrt{x}+\ C$

b)

$\frac{2}{5}x^3\sqrt{x}\ +\ C$

c)

$\sqrt{5x^4}\ +\ C$

d)

$\sqrt{\frac{1}{6}x^6}\ +\ C$

e)

$5x^{4\ }+\ C$

7.

a)

b)

c)

d)

8.

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

a)

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

b)

$-\tan x+C$

c)

$-\ln\left(1+x^2\right)+C$

d)

$\ln\left(1+x^2\right)+C$

9.

$\int e^xdx=$

a)

$e^{x+1}+C$

b)

$\ln x\ +\ C$

c)

$e^x+C$

d)

$\frac{e^{x+1}}{x+1}+C$

10.

$\int\frac{du}{u}=$

a)

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

b)

$u^o+C$

c)

$e^u+C$

d)

$\frac{1}{2}u^2+C$

11.

$\int\frac{dx}{\left|x\right|\sqrt{x^2-1}}=$

a)

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

b)

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

c)

$\sec x+C$

d)

$\csc x+C$

12.

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

a)

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

b)

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

c)

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

d)

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

13.

$\int\frac{6}{x^4}dx=....$

a)

$\frac{-2}{x^3}+c$

b)

$\frac{-3}{x^3}+c$

c)

$-2x^3+c$

d)

$-3x^3+c$

14.

$\int\left(2\ \sin\ x+18\right)dx=....$

a)

$-2\ \cos\ x+18\ x+C$

b)

$-\frac{1}{2}\cos\ x+\ 18\ x+C$

c)

$-9\ \cos\ x+18\ x+C$

d)

$\frac{1}{2}\cos\ x+18\ x+C$

e)

$2\ \cos\ x+18\ x+C$

15.

Determine the integral rule of the given expression:

a)

½c² + C

b)

ln|c| + C

c)

cx + C

d)

½cx² + C

TEST 2

Total questions: 15

Worksheet time: 11mins

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