# How do you find the area bounded by #y=x^2+2x-4# and #y=-2x^2+4x-3#?

##### 2 Answers

#### Explanation:

Consider the function:

The values of

Note now that as

The area bounded by the curves is then:

Use the integral of the difference between the two functions:

#### Explanation:

Here is a graph of

and

Pleases observe that equation [2] is greater than equation [1] in the enclosed region; this means that the integral is of the form:

Simplify the integrand:

We need to find the values of "a" and "b" by finding the two x coordinates where the two parabolas intersect. We can do this by setting the integrand equal to 0 and then solving for the two values of x:

Multiply by -1:

This factors into:

The above are the values of "a" and "b":