Question

if $I={\int }_0^{50\pi }\sqrt{1-cos2x}dx$, then the value of $\lambda$ is

• A. $50\sqrt{2}$
• B. $100$
• C. $0$
• D. $Noneofthese$

Answer 1

The correct option is D $Noneofthese$

$I={\int }_0^{50\pi }\sqrt{1-cos2xdx}$

$=\sqrt{2}{\int }_0^{50\pi }\left|sinx\right|dx$
$=50\sqrt{2}{\int }_0^{\pi }\left|sinx\right|dx$

$=50\sqrt{2}{\int }_0^{\pi }sinxdx=100\sqrt{2}$