# Thread: Help computing the area of a region bounded by the graphs of two function.

1. ## Help computing the area of a region bounded by the graphs of two function.

Question as is

Compute the area of the finite region bounded by the graphs of the functions

y=2x2 , and y=-2x2-8x+32

So i first set them equal to each other to find my points.

2x2=-2x2-8x+32

-4x2-8x+32=0

-4(x+4)(x-2)=0
x=-4, x=2

so when I integrate it will be from the limit of -4 to 2 right?

this is where I get stuck.

2. ## Re: Help computing the area of a region bounded by the graphs of two function.

$f_1(x) = 2x^2$

$f_2(x) = -2x^2 - 8x + 32$

$f_2(x) \geq f_1(x),~\forall x\in[-4,2]$

\begin{align*} \displaystyle &\phantom{=}\int_{-4}^2~f_2(x)-f_1(x)~dx \\ \\ &= \int_{-4}^2~-2x^2 - 8x + 32- 2x^2~dx \\ \\ &= \int_{-4}^2~-4x^2 - 8x + 32~dx \\ \\ &= \left . -\dfrac 4 3 x^3 - 4x^2 + 32x \right |_{-4}^2 \\ \\ &=144 \end{align*}

3. ## Re: Help computing the area of a region bounded by the graphs of two function.

thanks again.