# integral of a square root

• Oct 29th 2009, 08:20 PM
cottekr
integral of a square root
how do you find the integral of a square root of a polynomial?

specifically,

the integral of the sqaure root of (t^2+t^4)
• Oct 29th 2009, 08:23 PM
TheEmptySet
Quote:

Originally Posted by cottekr
how do you find the integral of a square root of a polynomial?

specifically,

the integral of the sqaure root of (t^2+t^4)

$\sqrt{t^2+t^4}=\sqrt{t^2(1+t^2)}=|t|\sqrt{1+t^2}$

We can find an antiderviative when $t \ge 0$ or when $t < 0$
• Oct 29th 2009, 08:46 PM
cottekr
in the problem I have, its a definite integral from 0 to 1. but I'm not sure how to find the integral of anything under the square root
• Oct 29th 2009, 09:21 PM
TheEmptySet
Quote:

Originally Posted by cottekr
in the problem I have, its a definite integral from 0 to 1. but I'm not sure how to find the integral of anything under the square root

$\int_{0}^{1}t\sqrt{1+t^2}dt$

let $u=1+t^2 \implies du=2tdt \iff \frac{1}{2}du=tdt$

$\int_{1}^{2}\sqrt{u}\frac{1}{2}du=\frac{1}{2}\int_ {1}^{2}u^{1/2}du...$