Question

Calculate integral below.

Integral ( square root of 25-x^2)dx from 0 to 5.

Answer 1

\[\int\limits_0^5 \left(\sqrt{25-x^2}\right) \, dx=\frac{25 \pi }{4} \]\[\int\limits \left(\sqrt{25-x^2}\right) \, dx=\frac{1}{2} x \sqrt{25-x^2}+\frac{25}{2} \text{ArcSin}\left[\frac{x}{5}\right] \]

Answer 2

Thank you.