# Thread: how would i integrate this

1. ## how would i integrate this

would i just integrate as normal, the double integral is putting me off.
could someone show me how id do:

$\int\limits_0^2 \int\limits_{x^{2}-2}^x x^{2} dydx$

thanks

2. Originally Posted by skystar
would i just integrate as normal, the double integral is putting me off.
could someone show me how id do:

$\int\limits_0^2 \int\limits_{x^{2}-2}^x x^{2} dydx$

thanks
The inside integral is constant with respect to y, so
$\int_0^2 \left ( \int_{x^{2}-2}^x x^2 dy \right ) dx$

$= \int_0^2 \left ( \left . x^2y \right |_{x^2 - 2}^x \right ) dx$

$= \int_0^2 \left ( x^2((x^2 - 2) - x ) \right ) dx$

I'm sure you can finish from here.

-Dan

$= \int_0^2 (x^4 - x^3 - 2x^2) dx$

3. Originally Posted by skystar
would i just integrate as normal, the double integral is putting me off.
could someone show me how id do:

$\int\limits_0^2 \int\limits_{x^{2}-2}^x x^{2} dydx$

thanks
Topsquark is right just remember that the $dx,dy,d\theta$ d whatever dictates what the variable of integration is...whatever variable is in the integral that is not of the same type as the d whatever is considered a constant

4. Originally Posted by Mathstud28
Topsquark is right just remember that the $dx,dy,d\theta$ d whatever dictates what the variable of integration is...whatever variable is in the integral that is not of the same type as the d whatever is considered a constant
What are you talking about ?