Download Using Integration to find the area between the curve and the x axis

Using Integration to find the
area between the curve and
the x axis between 2 points.

Start off with an equation
e.g.
4x  6x  6x  5
3

2
And where you want to
find the area between e.g.
1 and 5

To integrate, add 1 to the power,
then divide the co-efficient by
the new power.

So you need to follow these
simple steps:

Put the integration symbol in
front of the equation, along with
the two numbers you’re
integrating between (the largest
number on the top) and add
“dx” onto the end
5
4
x

6
x

6
x

5
dx

3
1
2

Now using square brackets, do what
I previously said about adding 1 to
the power and dividing the front
number by the new power, so you
get this.
5
 4x

6x
6x


 5x

2
2
 4
1
4
3
2

That simplifies to
x
4

5
 2 x  3x  5 x 1
3
2
which is easier to deal with

The next step is to put 5 as the x
value, and 1 as the x value, then
subtract the answer from 1 being
the x value from the answer you
get when 5 is the x value.

This is what you get when 5 and
1 are subbed in:
5  2  5  3 5  5  5
1  2 1  31  5 1
4
4
3
3
2
2

Simplify it down:
625  250  75  25 
1  2  3  5

Now you just need to do the
calculation, and you will have the
area, which is always in units2
unless stated otherwise.
975  11
 964units
2

You can check your answer
using derive for windows in the
maths department
Click
this
button
to open
this 
Enter the equation and the two limits
Now click simplify
and the answer will
come up on the
screen