Free Printable Integration

1.

Find the antiderivative of
4x-7

a)

4 +C

b)

2x²-7x+C

c)

x²-7x + C

d)

8x²+ C

2.

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.

3.

What does C represent in an antiderivative?

a)

A variable

b)

A constant

c)

None of these

d)

Unknown

4.

Find the antiderivative of
(1/3)x³-5x

a)

(1/12)x⁴-(5/2)x²+C

b)

(1/4)x⁴-(1/2)x²+C

c)

(1/12)x³-(5)x²+C

d)

(12)x⁴-(5)x²+C

5.

∫(4 - 18x)dx

a)

F(x) = -18

b)

F(x) = 4x - 9x²

c)

F(x) = 4x - 9x²+ C

d)

F(x) = (4 - 18x)² /2 + C

6.

INTEGRATE

a)

A

b)

B

c)

C

d)

D

7.

If y = $ax^n$ , then $\int_{ }^{ }y\ dx\ =$

a)

$\frac{ax^{n+1}}{n+1}$

b)

$\frac{ax^{n-1}}{n-1}+\ c$

c)

$\frac{ax^{n+1}}{n}+\ c$

d)

$\frac{ax^{n+1}}{n+1}+\ c$

8.

Which of the following is the indefinite integral of $\frac{x^3}{2}+7$ ?

a)

$\frac{3x^2}{2}$

b)

$\frac{3x^2}{2}+7x+c$

c)

$\frac{x^4}{8}+7x+c$

d)

$\frac{x^4}{8}+c$

9.

Integrate $\sqrt{x}$ with respect to x

a)

$x^{\frac{1}{2}}+c$

b)

$\frac{1}{2}x^{-\frac{1}{2}}+\ c$

c)

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

d)

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

10.

Which of the following is the indefinite integral of $\frac{3}{x^4}\ \ ?$

a)

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

b)

$\frac{3}{5x^5}+\ c$

c)

$-\frac{12}{x^5}+\ c$

d)

$\frac{1}{x^3}+\ c$

11.

Integrate $\int\left(2x+1\right)^{10}\ dx$ with respect to x.

a)

$22\left(2x+1\right)^{11}+c$

b)

$\frac{1}{22}\left(2x+1\right)^{11}+c$

c)

$11\left(2x+1\right)^{10}+c$

d)

$\frac{1}{11}\left(2x+1\right)^{10}+c$

12.

$\int_{ }^{ }\ \frac{1}{x}+\ \frac{1}{x^2}\ dx$

a)

$x^{-1}\ +\ x^{-2}+\ c$

b)

$x^0\ -\ x^{-1}+\ c$

c)

$\ln x+\ x^{-1}+\ c$

d)

$\ln x-\ x^{-1}+\ c$

13.

$\int_{ }^{ }\sec^2\ 5x\ \ dx\ \ =$

a)

$\tan\ x\ \ +\ c$

b)

$\frac{1}{5}\tan\ x\ \ +\ c$

c)

$\frac{1}{5}\tan\ 5x\ \ +\ c$

d)

$\frac{1}{5}\tan^2\ 5x\ \ +\ c$

14.

Integrate $\sin\left(\frac{x}{2}\right)$ with respect to x

a)

$\cos\left(\frac{x}{2}\right)\ +\ c$

b)

$-2\cos\left(\frac{x}{2}\right)\ +\ c$

c)

$-\cos\left(\frac{x}{2}\right)\ +\ c$

d)

$-\frac{1}{2}\cos\left(\frac{x}{2}\right)\ +\ c$

15.

Find the integral with respect to x of $\int_{ }^{ }\ \left(e^{3x}\right)^2\ dx\ .$

a)

$\frac{e^{6x}}{6}\ +\ c$

b)

$\frac{e^{9x}}{9}\ +\ c$

c)

$6e^{6x}\ +\ c$

d)

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

16.

Find indefinite integral for $\int_{ }^{ }\frac{1}{e^{5x}}\ dx$

a)

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

b)

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

c)

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

d)

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

17.

∫3x²(x³-9)^2/3 dx

a)

(3x²)^4/3

b)

(2/3)(x³-9)^5/3

c)

3(x³-9)^-1/3

d)

-3(x³-9)^-1/3

18.

∫e^xsin(e^x+6) dx

a)

-cos(e^x+6) + C

b)

cos(e^x+6) +C

c)

sin(e^x+6)+C

d)

e^2x/2

19.

$\frac{d}{dx}\left[e^{2x}\ +\ 3x^2+5\right]$

a)

$e^{2x}+\ 6x^2$

b)

$2e^{2x}\ +6x\$

c)

$2e^x+6x\$

d)

none of these

20.

$\int_{ }^{ }e^{5x}dx\ =$

a)

$e^{5x}+c$

b)

$5e^{5x}+c$

c)

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

d)

none of these

Integration

Total questions: 20

Worksheet time: 5hrs 0mins

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