Free Printable Indefinite Integral: Power Formula

1.

Determine the integral rule of the given expression:

a)

n*x^n-1 + C

b)

(n+1)*xⁿ⁺¹ + C

c)

¹/_n-1 * x^n-1 + C

d)

¹/_n+1 * xⁿ⁺¹ + C

2.

Determine the integral rule of the given expression:

a)

x^-2 + C

b)

^-2/_x³ + C

c)

^-1/_x + C

d)

²/_x + C

3.

Determine the integral rule of the given expression:

a)

x^1/2+ C

b)

¹/_(2√x) + C

c)

³/₂*x^3/2 + C

d)

²/₃*x^3/2 + C

4.

Determine the integral rule of the given expression:

a)

^-1/_x² + C

b)

lnx + C

c)

ln|x| + C

d)

^-1/_x + C

5.

Determine the integral rule of the given expression:

a)

½c² + C

b)

ln|c| + C

c)

cx + C

d)

½cx² + C

6.

What is an Antiderivative?

a)

The opposite of a derivative

b)

The same as a derivative

c)

A second derivative

d)

It always represents velocity

7.

When do you add C when finding Antiderivatives?

a)

Never

b)

Sometimes

c)

Always

d)

Seldom

8.

What does C represent in an Antiderivative?

a)

A variable

b)

Unknown

c)

A constant

d)

None of these

9.

Find the Antiderivative of $\frac{1}{3}x^3-5x$ .

a)

$12x^4-5x^2+C$

b)

$\frac{1}{12}x^4-\frac{5}{2}x^2+C$

c)

$\frac{1}{12}x^3-5x^2+C$

d)

$\frac{1}{12}x^4-5x^2+C$

10.

Integrate $\int\left(-20x^3-6x^{-3}\right)dx$

a)

$-5x^4+\frac{3}{x^2}+C$

b)

$-20x^4-\frac{6}{x^2}+C$

c)

$-5x^3+\frac{3}{x^3}+C$

d)

$-20x^4+\frac{3}{2}+C$

11.

∫ 4 dx

a)

0

b)

4t + C

c)

4x + C

d)

2x² + C

12.

a)

1/x²+C

b)

x²+C

c)

-1/x²+C

d)

C

13.

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

a)

$\frac{4}{3}x^3-3x^2+9x+c$

b)

$\ \frac{4}{3}x^3+3x^2+9x\ +\ c$

c)

$\frac{4}{3}x^3-6x^2-9x+c\$

d)

$\frac{4}{3}x^3+6x^2+9x+c$

e)

$\frac{3}{4}x^3+6x^2-9x+c$

14.

$\int\left(\frac{4}{5}x^3-\ 4x^2+\frac{4}{x^2}-7\right)dx\ =\ ...$

a)

$\frac{1}{5}x^4-\frac{4}{3}x^3-4x^{-1}-7x\ +\ c$

b)

$\frac{1}{5}x^4-\frac{4}{3}x^3+4x^{-1}-7x+c$

c)

$\frac{1}{5}x^4-\frac{4}{3}x^3-4x^{-1}-7+c$

d)

$\frac{1}{5}x^4-8x^3-\frac{4}{3}x^2-7x+c$

e)

$\frac{12}{5}x^4-8x^3-4x^{-1}-7x+c$

15.

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

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)

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

16.

∫ 7 dx=

a)

7x + c

b)

7 / 2 x²+ c

c)

4x+c

d)

3x+c

17.

∫ 2x³ dx =

a)

1 / 2 x⁴ + c

b)

x⁴+c

c)

x²+x+c

d)

x+c

18.

∫ 8x³ - 3x² + x + 5 dx=

a)

2x⁴+3x³+c

b)

3x²+c

c)

4x²+ x+c

d)

2x⁴ - x³ + 1 2 x² + 5x + c

19.

∫ (2x + 1)(x - 5) dx=

a)

x³+x²+x+c

b)

2 / 3 x³ + 9 / 2 x² - 5x + c

c)

1 / 3 x⁴+ 1 / 2 x +c

d)

x²+c

20.

∫ (5x+1)¹⁰ dx =

a)

2 / 33 ( 5x+1)¹⁰ + c

b)

1 / 55 ( 5x +1 )¹¹+ c

c)

2 / 3 ( 5x+1)⁹ +c

d)

3 / 5 ( 5x+1)¹²+ c

21.

$\int t^2\left(3t+5\right)dt=....$

a)

$\frac{3}{4}t^4+\frac{5}{3}t^3+c$

b)

$3t^4+\frac{3}{5}t^3+c$

c)

$\frac{3}{4}t^3+\frac{5}{3}t^2+c$

d)

$9t^2+10t+c$

22.

$\int\left(6x^2+10x\right)dx=....$

a)

$2x^3+5x^2+c$

b)

$3x^3+5x^2+c$

c)

$2x^3+10x^2+c$

d)

$2x^3-5x^2+c$

23.

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

a)

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

b)

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

c)

$-2x^3+c$

d)

$-3x^3+c$

24.

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

a)

$6x^3+2x^2+3+C$

b)

$2x^3+x^2+3+C$

c)

$6x^3+2x^2+3x+C$

d)

$2x^3+x^2+3x+C$

25.

$\int_{ }\left(\frac{4}{3x-6}\right)dx$

a)

$4\ \ln\ \left(3x-6\right)+C$

b)

$\frac{4}{3}\ln\left(3x-6\right)+C$

c)

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

d)

$3\ \ln\ \left(3x-6\right)+C$

Indefinite Integral: Power Formula

Total questions: 25

Worksheet time: 29mins

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