Property 26
\(x^2+y^2=r^2\)
\(\blacksquare\quad\displaystyle\int\limits_{-r}^{r} \sqrt{r^2-x^2}\,dx=\samefrac{\pi r^2}2\)
\(\blacksquare\quad\displaystyle\int\limits_{0}^{r} \sqrt{r^2-x^2}\,dx=\samefrac{\pi r^2}4\)
1.
\(\displaystyle\int\limits_{0}^{2} \sqrt{4-x^2}\,dx=?\)
2.
\(\displaystyle\int\limits_{-3}^{3} \sqrt{9-x^2}\,dx=?\)
3.
\(\displaystyle\int\limits_{0}^{7} \sqrt{49-x^2}\,dx=?\)
4.
\(\displaystyle\int\limits_{0}^{2\sqrt2} \sqrt{16-x^2}\,dx=?\)
5.
\(\displaystyle\int\limits_{0}^{\sqrt2} \sqrt{4-x^2}\,dx=?\)
6.
\(\displaystyle\int\limits_{0}^{3} (\sqrt{36-x^2}-\sqrt3x)\,dx=?\)