![\int _{-5r}^{5r}\:\left[\:2\sqrt{\left(25r^2\:-\:x^2\right)}\:\right]\:^2\:dx\\=\int _{-5r}^{5r}4\left(25r^2-x^2\right)dx\\\\= 4\cdot \int _{-5r}^{5r}25r^2-x^2dx\\\\= 4\left(\int _{-5r}^{5r}25r^2dx-\int _{-5r}^{5r}x^2dx\right)\\\\= 4\left(250r^3-\frac{250r^3}{3}\right)\\\\= 4\cdot \frac{500r^3}{3}\\\\= \frac{2000r^3}{3}](/tpl/images/0745/5172/e2da8.png)
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