Question

Evaluate ${\int }_0^{100\pi }\sqrt{(1-\cos 2x)}dx$

Answer 1

${\int }_0^{100\pi }\sqrt{1-\cos 2x}dx$

$={\int }_0^{100\pi }\sqrt{2}|\sin x|dx$

$=\left(\sqrt{2}\right)\left(100\right){\int }_0^{100\pi }\sin xdx$

$=100\sqrt{2}[-\cos x{]}_0^{\pi }$

$=200\sqrt{2}$