integral of a square root

**cottekr** · October 29th 2009, 07:20 PM

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)

**TheEmptySet** · October 29th 2009, 07:23 PM

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 $t < 0$

**cottekr** · October 29th 2009, 07:46 PM

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

**TheEmptySet** · October 29th 2009, 08:21 PM

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

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

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