Thread: integral of a square root

1. 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)

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

We can find an antiderviative when $\displaystyle t \ge 0$ or when $\displaystyle t < 0$

3. 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

4. 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
$\displaystyle \int_{0}^{1}t\sqrt{1+t^2}dt$

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

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