Free Printable Ch. 6 - Integration of exponential, log & trigo. function

1.

$\int_{ }2\sin\ 7x\ dx\ =$

a)

$7\cos\ 7x\ +\ C$

b)

$2\cos\ 7x\ +\ C$

c)

$\frac{2}{7}\cos\ 7x\ +\ C$

d)

$-\frac{2}{7}\cos\ 7x\ +\ C$

2.

$\int_{ }^{ }2\cos\left(6+3x\right)\ dx\ =$

a)

$\frac{2}{6}\sin\ \left(6+3x\right)\ +\ C$

b)

$\frac{1}{6}\sin\ \left(6+3x\right)\ +\ C$

c)

$\frac{2}{3}\sin\ \left(6+3x\right)\ +\ C$

d)

$\frac{2}{3x}\sin\ \left(6+3x\right)\ +\ C$

3.

Evaluate: $∫(5\sin⁡x-4\cos⁡x)dx$

a)

$5\sin⁡x-4\cos⁡x+C$

b)

$-5\cos⁡x-4\sin⁡x+C$

c)

$5\cos⁡x+4\sin⁡x+C$

4.

Evaluate: $∫\sin⁡θ\cot⁡θdθ$

a)

$\sin⁡θ+C$

b)

$\cos⁡θ+C$

c)

$\cot⁡θ+C$

5.

$\int_{ }^{ }\tan xdx$

a)

cotx + C

b)

$\sec^2x+C$

c)

ln|secx| +C

d)

ln|cosx| +C

6.

\int_{ }^{ }\sin^34xdx

a)

$-\frac{1}{4}\cos4x+\frac{1}{12}\cos^34x\ +C$

b)

$\frac{1}{4}\cos4x+\frac{1}{12}\cos^34x\ +C$

c)

$-\frac{1}{4}\cos4x-\frac{1}{12}\cos^34x\ +C$

d)

none of the above

7.

\int_{ }^{ }\sin^42x\cos^22xdx

a)

$\frac{1}{16}x+\frac{1}{128}\sin8x-\frac{1}{96}\sin^34x+C$

b)

$\frac{1}{16}x-\frac{1}{128}\sin8x-\frac{1}{96}\sin^34x+C$

c)

$\frac{1}{16}x-\frac{1}{128}\sin8x+\frac{1}{96}\sin^34x+C$

d)

none of the above

8.

For the indicated integral, what would the first step be?

a)

Save a sine and convert the rest to cosines

b)

Save a cosine and convert the rest to sines

c)

Use u-substitution

d)

Just integrate

9.

\int_{ }^{ }\left(\frac{e^{4x^{-2}}}{x^3}\right)dx

a)

$\frac{-1}{8}e^{4x^{-2}}+C$

b)

$\frac{1}{8}e^{4x^{-2}}+C$

c)

$-8e^{4x^{-2}}+C$

d)

none of the above

10.

$\int_{ }^{ }\frac{1}{\sqrt{x}}e^{\sqrt{x}}dx$

a)

$\frac{2}{\sqrt{x}}e^{\sqrt{x}}+C$

b)

$\frac{1}{2\sqrt{x}}e^{\sqrt{x}}+C$

c)

$\frac{1}{2}e^{\sqrt{x}}+C$

d)

$2e^{\sqrt{x}}+C$

11.

$\int_{ }^{ }\frac{e^{\ln\left|x\right|}}{x}dx$

a)

$x+C$

b)

$\frac{1}{x}e^{\ln\left|x\right|}+C$

c)

$e^{\left|x\right|}+C$

d)

None

12.

$\int_{ }^{ }\left(e^{-x}+3\right)^4e^{-x}dx$

a)

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

b)

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

c)

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

d)

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

13.

Integrate the partial fraction with respect to x
$\int_{ }^{ }\ \frac{1}{\left(x\right)}\ +\ \frac{4}{\left(2x\ -1\ \right)}\ dx$

a)

$\ln\ \left|x\right|\ +\ 8\ \ln\left|2x-1\right|+c$

b)

$\ln\ \left|x\right|\ +\ 4\ \ln\ \left|x-1\right|+c$

c)

$\ln\ \left|x\right|\ +\ 4\ \ln\left|2x-1\right|+c$

d)

$\ln\ \left|x\right|\ +\ 2\ \ln\left|2x-1\right|+c$

14.

$\int\left(5\sqrt{x^3}-16e^{-4x}+\frac{1}{x}\right)dx$

a)

$2x^{\frac{5}{2}}+4x^{-4x}+\ln\left|x\right|+C$

b)

$5x^{\frac{1}{3}}+4e^{-4x}+\ln\left|x\right|+C$

c)

$2x^{\frac{5}{2}}-4e^{-4x}+\ln\left|x\right|+C$

d)

Nothing is correct

15.

Solve $\int_{ }\frac{\left(\ln3x\right)^4}{x}dx$

a)

$\frac{\ln\left(3x\right)^5}{5}+C$

b)

$\frac{\left(\ln3x\right)^5}{5}+C$

c)

$\ln3x+C$

d)

$\frac{\left(\ln3x\right)^5}{15}+C$

Ch. 6 - Integration of exponential, log & trigo. function

Total questions: 15

Worksheet time: 8mins

Similar Resources on Wayground