Question

Let $I=\underset{0}{\overset{100\pi }{\int }}\sqrt{1-\cos 2x}dx$, then

• A. $I=0$
• B. $I=200\sqrt{2}$
• C. $I=\pi \sqrt{2}$
• D. $I=100$

Answer 1

The correct option is B $I=200\sqrt{2}$

$1-\cos 2x=2{\sin }^{2}x\Rightarrow I=\underset{0}{\overset{100\pi }{\int }}\sqrt{2}|\sin x|dx=100\sqrt{2}{\int }_0^{\pi }|\sin x|dx$
$\Rightarrow I=200\sqrt{2}$