# Math Help - How do you find the area bounded by y coordinates?

1. ## How do you find the area bounded by y coordinates?

How do you find the area bounded by

y= 4x^3 and y= 12x^2-8x

2. Originally Posted by cnyce05
How do you find the area bounded by

y= 4x^3 and y= 12x^2-8x
The graphs intersect three times. If you solve $4x^3=12x^2-8x$ you find that they intersect at $x=0,1,2$

$f(x)=4x^3$

$g(x)=12x^2-8x$

So you will have to use two integrals. The cubed function is greater than the parabola on the interval $[0,1]$ and the parabola is greater on the interval from $[1,2]$. This is obvious if you graph it on a calculator. Or you can just use test values. The area should be:

$\int_0^1 [4x^3-(12x^2-8x)]dx + \int _1^2 [(12x^2-8x)-4x^3]dx$