# Thread: Area Between Two Curves

1. ## Area Between Two Curves

Hi guys,

I have a problem that I have failed solve and it involves finding the area of the region enclosed by the two curves: $\displaystyle x^4$ and $\displaystyle 2x^2 + 1$

I do know that I need to integrate these two functions, however I am unable to find the bounds.

I know that you must set them equal to each other, but I can't seem to find a value.

-Christian

2. Are you sure those are the functions?
It seems odd that you'd be given functions so messy.

Anyways. You have;

$\displaystyle x^4-2x^2-1=0$

The use the quadratic formula of the form
$\displaystyle x^2=-b+-...etc...$ you know thw rest

And you should end up with 4 solutions, however two of them are not real.
Then you have:

$\displaystyle x=sqrt(1+sqrt(2))$ and $\displaystyle x=-sqrt(1+sqrt(2))$

3. Ya, this professor likes to make your life hard!

That makes sense...you should get two values, because they are both parabolas.

Thanks a bunch for clearing this up!

-Christian