Free Printable Integration Quiz 1

1.

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)

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

2.

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)

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

3.

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

a)

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

b)

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

c)

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

d)

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

4.

$\int5x^4dx$

a)

$x^5$

b)

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

c)

$x^5+C$

d)

$20x^3$ + C

5.

$\int\left(x^2-2x\right)dx$

a)

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

b)

$x^{2\ }-2x+C$

c)

$2x-2$

d)

$\frac{1}{3}x^3-x^2$

6.

$\int6x\left(x+2\right)dx$

a)

$6x^2+12x+C$

b)

$x^{2\ }-2x+C$

c)

$3x^2+6x+C$

d)

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

7.

$\int\left(6\sqrt{x}-1\right)dx$

a)

$6x^{\frac{3}{2}}+x+C$

b)

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

c)

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

d)

I didn't look at my notes to see how to do this one.

8.

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

a)

$-x^{-1}-3x^{-2}+C$

b)

$\frac{x^{-3}}{-3}+\frac{6x^{-4}}{-4}+C$

c)

$-x^{-1}-3x^{-2}$

d)

$-x-3x^2+C$

9.

$\int\left(5x^2-7x+6\right)dx$

a)

$\frac{5}{3}x-\frac{7}{2}x+6x+C$

b)

$x+x+x+x+x+C$

c)

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

d)

$\frac{5}{3}x^3-\frac{7}{2}x^2+6x+C$

10.

$\int4\sin\left(-x\right)dx$

a)

$4\cos\left(x\right)+C$

b)

$-4\sin\left(-x\right)+C$

c)

$4\cos\left(-x\right)+C$

d)

$-4\cos\left(-x\right)+C$

11.

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

a)

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

b)

$5x^{\frac{1}{3}}-4e^{-4x}+1+C$

c)

$\frac{5}{2}x^{\frac{3}{2}}-16e^{-4x}+\ln\left|x\right|+C$

d)

Got lazy with fake answers

12.

$\int8x^{-3}dx$

a)

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

b)

$4x^{-3}+C$

c)

$\frac{8}{-3}x^{-2}$

d)

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

13.

$\int\left(x^{-1}-1\right)dx$

a)

$\ln\left|x\right|-x+C$

b)

$\frac{x^{-2}}{-2}-x+C$

c)

$\ln\left|x\right|-1+C$

d)

$1-x+C$

14.

$\int0dx$

a)

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

b)

$Not\ Possible$

c)

$x+C$

d)

$C$

15.

Find the answer of ∫x²+4x dx?

a)

X³/2+2x²

b)

X²+4x

c)

x²/2 +3x+C

d)

x³/3+2x²+C

16.

Integrate $\int_{ }^{ }x^{\frac{1}{3}}dx$

a)

$=\frac{4}{3}x^{\frac{4}{3}}+c$

b)

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

c)

$=\frac{1}{3}x^{-\frac{2}{3}}+c$

d)

$=\frac{3}{4}x^{\frac{4}{3}}+c$

17.

Integrate $\int_{ }^{ }\sin x\ dx$

a)

$=\tan x+c$

b)

$=-\cos x+c$

c)

$=-\sec x+c$

d)

$=\operatorname{cosec}\ x\ +c$

18.

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

a)

$=\ln2x+c$

b)

$=2\ \ln2x+c$

c)

$=\frac{1}{2}\ln2x+c$

d)

$=\frac{1}{\ln2x}+c$

19.

$\int\tan x_{ }dx\$

a)

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

b)

$-\ln\left|\cos x\right|+C$

c)

$\ln\left|\sin x\right|+c$

d)

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

20.

$\int\left(\frac{4}{x}-e_{ }^x\right)dx$

a)

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

b)

$4\ln\left|x\right|-e^x+C$

c)

$4\ln\left(x\right)-e^x+C$

d)

$4\ln\left|x\right|+e^x+C$

21.

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.

22.

What does C represent in an antiderivative?

a)

A variable

b)

A constant

c)

None of these

d)

Unknown

23.

∫(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

24.

∫(3x⁴+2)⁴(12x³)dx

a)

½(3x⁴+2)⁴+C

b)

(3x⁴+2)⁴+C

c)

⅕(3x⁴+2)⁵+C

d)

⅓(3x⁴+2)⁶+C

25.

Integrate $\int_{ }^{ }3\ dx$

a)

= 0

b)

$=\frac{3}{x}+c$

c)

$=\ 3x\ +c$

d)

$=4+c$

26.

Integrate $\int_{ }^{ }\left(x^2+7\right)dx$

a)

$=2x+c$

b)

$=x^3+7x$

c)

$=\frac{1}{2}x^3+7x$

d)

$=\frac{1}{3}x^3+7x+c$

27.

$\int\left(\frac{4}{x}-e_{ }^x\right)dx$

a)

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

b)

$4\ln\left|x\right|-e^x+C$

c)

$4\ln\left(x\right)-e^x+C$

d)

$4\ln\left|x\right|+e^x+C$

28.

$\int\cos\left(3-4x\right)dx_{ }^{ }$

a)

$\frac{1}{4}\sin\left(3-4x\right)+C$

b)

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

c)

$-\frac{1}{4}\sin\left(3-4x\right)+C$

d)

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

29.

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)

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

30.

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

a)

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

b)

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

c)

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

d)

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

31.

∫ - sinx dx

a)

-cos x + C

b)

cos x + C

c)

tan x + C

d)

1/√1- x²

32.

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

a)

$e^{5x}+c$

b)

$5e^{5x}+c$

c)

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

d)

none of these

33.

$\int\ \frac{2}{x+3}dx^{ }=$

a)

2ln|x+3|

b)

2ln(x + 3) + c

c)

$\frac{1}{2}\ln\left|x\ +\ 3\right|\ +\ c$

d)

none of these

34.

Integrate $\int_{ }^{ }x^{\frac{1}{3}}dx$

a)

$=\frac{4}{3}x^{\frac{4}{3}}+c$

b)

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

c)

$=\frac{1}{3}x^{-\frac{2}{3}}+c$

d)

$=\frac{3}{4}x^{\frac{4}{3}}+c$

35.

Which of the following is TRUE ?

a)

$\int_{ }^{ }\sin\ x\ \ dx\ =\ \cos\ x\ +c$

b)

$\int_{ }^{ }e^x\ \ dx\ =\ \frac{e^{x+1}}{x+1}\ +\ c$

c)

$\int_{ }^{ }\ \frac{1}{x}\ \ dx\ =\ \ln\ \left|x\ \right|\ +c$

d)

$\int_{ }^{ }\ x\ \ dx\ =\ 1\ +\ c$

36.

$\int_{ }^{ }x^3\ -\pi\ dx\ \ =$

a)

$3x^2\ +\ c$

b)

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

c)

$\frac{x^4}{4}\ -\ \pi x$

d)

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

37.

Which of the following is NOT one of techniques of Integration?

a)

Substitution

b)

By Part

c)

Quotient Rule

d)

Partial Fraction

38.

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)

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

39.

Evaluate $\int_1^2\ \ 3x^2\ \ dx$

a)

$7$

b)

$8$

c)

$12$

d)

$x^3$

40.

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

a)

$2$

b)

$4$

c)

$6$

d)

$8$

Integration Quiz 1

Total questions: 40

Worksheet time: 59mins

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