Wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Basic Integration

Total questions: 12

Worksheet time: 35mins

Name
Class
Date
1.

∫5x4dx\int5x^4dx  

a)

x5x^5  

b)

54x5+C\frac{5}{4}x^5+C  

c)

x5+Cx^5+C  

d)

20x320x^3  + C

2.

∫(x2−2x)dx\int\left(x^2-2x\right)dx  

a)

13x3−x2+C\frac{1}{3}x^3-x^2+C  

b)

x2 −2x+Cx^{2\ }-2x+C  

c)

2x−22x-2  

d)

13x3−x2\frac{1}{3}x^3-x^2

3.

∫6x(x+2)dx\int6x\left(x+2\right)dx  

a)

6x2+12x+C6x^2+12x+C  

b)

x2 −2x+Cx^{2\ }-2x+C  

c)

3x2+6x+C3x^2+6x+C  

d)

2x3+6x2+C2x^3+6x^2+C

4.

∫(5x2−7x+6)dx\int\left(5x^2-7x+6\right)dx  

a)

53x−72x+6x+C\frac{5}{3}x-\frac{7}{2}x+6x+C  

b)

x+x+x+x+x+Cx+x+x+x+x+C  

c)

x3−3x2+6x+Cx^3-3x^2+6x+C  

d)

53x3−72x2+6x+C\frac{5}{3}x^3-\frac{7}{2}x^2+6x+C  

5.

Integrate ∫sin⁡x dx\int_{ }^{ }\sin x\ dx  

a)

=tan⁡x+c=\tan x+c  

b)

=−cos⁡x+c=-\cos x+c  

c)

=−sec⁡x+c=-\sec x+c  

d)

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

6.

∫(cos x + 3x2)dx =

a)

-sin x + x3 + c

b)

sinx + x3 + c

c)

-sin x + 6x

d)

🌞

7.
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.
8.
What does C represent in an antiderivative?
a)
A variable
b)
A constant
c)
None of these
d)
Unknown
9.

Integrate ∫3 dx\int_{ }^{ }3\ dx  

a)

= 0

b)

=3x+c=\frac{3}{x}+c  

c)

= 3x +c=\ 3x\ +c  

d)

=4+c=4+c  

10.

Integrate ∫x13dx\int_{ }^{ }x^{\frac{1}{3}}dx  

a)

=43x43+c=\frac{4}{3}x^{\frac{4}{3}}+c  

b)

=32x23+c=\frac{3}{2}x^{\frac{2}{3}}+c  

c)

=13x−23+c=\frac{1}{3}x^{-\frac{2}{3}}+c  

d)

=34x43+c=\frac{3}{4}x^{\frac{4}{3}}+c  

11.

If y = axnax^n  , then ∫y dx =\int_{ }^{ }y\ dx\ =  

a)

axn+1n+1\frac{ax^{n+1}}{n+1}  

b)

axn−1n−1+ c\frac{ax^{n-1}}{n-1}+\ c  

c)

axn+1n+ c\frac{ax^{n+1}}{n}+\ c  

d)

axn+1n+1+ c\frac{ax^{n+1}}{n+1}+\ c  

12.

Integrate x\sqrt{x} with respect to x

a)

x12+cx^{\frac{1}{2}}+c  

b)

12x−12+ c\frac{1}{2}x^{-\frac{1}{2}}+\ c  

c)

23x32+ c\frac{2}{3}x^{\frac{3}{2}}+\ c  

d)

32x32+ c\frac{3}{2}x^{\frac{3}{2}}+\ c