Free Printable Calculus Integration of log.& Exp.

1.

Simplify the expression $\ln\left(e^{3x}\right)$ .

a)

$3\ln\left(e^{3x}\right)$

b)

$\ln\left(3x\right)$

c)

$e^{3x}$

d)

$3x$

2.

a)

b)

c)

d)

3.

a)

b)

c)

d)

4.

What is $\int_{ }^{ }\ \frac{5}{x^6}\ dx$ ?

a)

$5x^{-6}\ +\ c$

b)

$5x^{-5}\ +\ c$

c)

$-\frac{5}{4x^4}\ +\ c$

d)

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

5.

Evaluate the integral $\int_0^2\ \frac{x^3\ +\ x^2}{x^2}\ dx$

a)

$2$

b)

$4$

c)

$6$

d)

$8$

6.

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

a)

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

b)

$-\tan x+C$

c)

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

d)

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

7.

$\int dx=$

a)

$0$

b)

$x+C$

c)

$1$

d)

$undefined$

8.

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

a)

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

b)

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

c)

$\ln\left|x^2+1\right|+C$

d)

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

9.

$\int-\csc^2xdx$

a)

$\frac{1}{3}\csc^3x+C$

b)

$\cot x+C$

c)

$-\cot x+C$

d)

$\csc x\cot x+C$

10.

$\frac{\text{d}}{\text{d}x}\left(\sec x\right)=$

a)

$\sec x\tan x$

b)

$\sec^2x$

c)

$\tan^2x$

d)

$\frac{1}{2}\sec^2x$

11.

$\int u^ndu=$

a)

$\ln u+C$

b)

$u^{n+1}+C$

c)

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

d)

$u^{n-1}+C$

12.

$\frac{\text{d}}{\text{d}x}\left(\ln\left|x\right|\right)=$

a)

$e^x$

b)

$-x^{-1}$

c)

$-x^{-2}$

d)

$\frac{1}{\left|x\right|}$

13.

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

a)

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

b)

$u^o+C$

c)

$e^u+C$

d)

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

14.

$\int e^xdx=$

a)

$e^{x+1}+C$

b)

$\ln x\ +\ C$

c)

$e^x+C$

d)

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

15.

∫cos(4x+5)dx

a)

-¼sin(4x + 5) + C

b)

4sin(4x + 5) + C

c)

¼sin(4x + 5) + C

d)

4cos(4x + 5) + C

16.

a)

62

b)

64/11

c)

56/3

d)

50/3

17.

Evaluate the indefinite integral.

a)

A

b)

B

c)

C

d)

D

18.

a)

(x¹¹⁄ 11) - 1

b)

(x¹⁰) - 1

c)

x¹⁰

d)

t¹¹ ∕ 11

19.

What can be calculated using this expression?

a)

Intermediate Value of F

b)

Instantaneous Rate of Change

c)

Average Rate of Change

d)

Average Value of f

20.

Evaluate: ∫sec²(x) dx

a)

sec(x) + C u²

b)

tan(x) + C u²

c)

⅓sec³(x) + C u²

d)

½tan²(x) + C u²

21.

Find the area of the region enclosed by the lines and curves.

y = 3x + 4 and y = x² + 4

a)

9

b)

93/2

c)

9/2

d)

18

22.

∫ 2 x (x²- 3)^(1/2) dx

a)

(x²- 3)^(3/2⁾+C

b)

(3/2)(x²- 3)^(3/2)+C

c)

(2/3)(x²- 3)^(3/2)+C

d)

(2/3)(x²- 3)^(-1/2)+C

23.

∫ e^2x dx

a)

e^2x +C

b)

2e^2x + C

c)

(1/2)e^{x + C}

d)

(1/2)e^2x +C

24.

Find the derivative.

a)

b)

c)

d)

25.

Evaluate.

a)

b)

c)

d)

e)

26.

Evaluate.

a)

b)

c)

d)

e)

27.

Find the derivative.

a)

b)

c)

d)

e)

28.

Evaluate.

a)

b)

c)

d)

e)

29.

Evaluate.

a)

b)

c)

d)

e)

30.

Evaluate.

a)

b)

c)

d)

e)

31.

Evaluate

a)

b)

c)

d)

e)

32.

Evaluate.

a)

b)

c)

d)

e)

Calculus Integration of log.& Exp.

Total questions: 32

Worksheet time: 1hrs 15mins

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