# Math Help - Integral of function involving root

1. ## Integral of function involving root

Hi guys,

Would appreciate some help in explaining how to evaluate $\int\sqrt{4{r}^2-{r}^4}\, dr$.

2. ## Re: Integral of function involving root

Originally Posted by aforl
Hi guys,

Would appreciate some help in explaining how to evaluate $\int\sqrt{4{r}^2-{r}^4}\, dr$.
1.

$\int\sqrt{4{r}^2-{r}^4}\, dr = \int(|r| \cdot \sqrt{4-{r}^2})\, dr = -{\frac12}\int(-2|r| \cdot \sqrt{4-{r}^2})\, dr$

2. You have to consider two different cases: r is positive or zero or r is negative.

3. Use now integration by substitution with $u = 4-r^2$.