Learning Enhancement Team
Worksheet:
Integrating y  ax n
This worksheet has questions about integration using the power rule which allows you
to integrate functions form ax n .
Integrating y  ax n
Model solutions to
this sheet
1.
study guide
Do the following integrations:
a)
3
 4x dx
b)
2
 6x dx
c)

x2
dx
6
d)
 4xdx
e)
 5x
f)
 4dx
g)
 0.7dx
h)
 2 dx
j)
x
k)
x
l)
 x dx
i)
4
 3 xdx
3
x
4
dx
2
3
dx
1
2
dx
1
2.
Now differentiate all your answers to question 1. What do you notice?
3.
Integrate the following equations to find y in terms of x and a constant:
a)
dy
 4x 3
dx
4.
Do the following integrations:
a)
 4 d
b)
3
e)
5  x2
 x dx
f)
 v  3 dv
3
b)
dy
4
dx
A dA
2
c)
dy x

dx 3
c)

g)
5
A
dA
d)
dy
4

dx 3 x
d)
 3s
2
x3  3 3  x3
 2  2 dx
This worksheet is one of a series on
mathematics produced by the Dean of
Students' Office at the University of East
Anglia.
Scan the QR-code with a smartphone to go
to the Learning Enhancement Team website.
2
ds