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Math Help - Integral of function involving root

  1. #1
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    Integral of function involving root

    Hi guys,

    Would appreciate some help in explaining how to evaluate \int\sqrt{4{r}^2-{r}^4}\, dr.
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  2. #2
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    Re: Integral of function involving root

    Quote Originally Posted by aforl View Post
    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.
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