# Thread: Area between the curves

1. ## Area between the curves

I am asked to find the area between the two curves below with respect to [0,1].

y = (((x^2)((x^3)+1)^10)/11)+3

and

y = (-((x)((x^2)+1)^10)/11)+3

I am having a lot of difficulty finding the integral.

Thanks

Alex

2. Having you drawn the picture?

3. Yes I drew it and plugged it into my calculator and it looks like a number that is not countable. I made a mistake with my formulas though in the above post that i will correct.

4. The formula for integrating the area between two curves is

$\int_{a}^{b}[f(x)-g(x)]dx$

Where f(x) is the top curve and g(x) is the bottom curve.

or
$\int_{a}^{b}\int_{g_1(x)}^{g_2(x)}f(x,y)dydx$

5. Okay, that I know

Then you end up with an integral that I do not know how to solve which is my problem...

You get the integral of

(((x^2)(x^3+1)^10)/11)+(((x)(x^2+1)^10)/11)

This is where I am stuck.. Finding the answer to the above integral.

6. If you can't combine them, break them up into two separate integrals and add the results of both integrals.

7. Originally Posted by alex.caine
Okay, that I know

Then you end up with an integral that I do not know how to solve which is my problem...

You get the integral of

(((x^2)(x^3+1)^10)/11)+(((x)(x^2+1)^10)/11)

This is where I am stuck.. Finding the answer to the above integral.

Nevermind.

8. Then, once you have two integrals, use u-sub to simplify your integrals

9. Could you please inform me what u-sub is

10. substitution

11. I do not know the formula for that...
If anyone other than dsmith could be of assistance it would be greatly appreciated