intlimits_0^{pi /4} {sin ,,2x,,dx} સદીશનું મૂ | vedclass

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Question

$\int\limits_0^{\frac{\pi }{4}} {\sin {\mkern 1mu} {\mkern 1mu} 2x{\mkern 1mu} {\mkern 1mu} dx{\mkern 1mu} {\mkern 1mu}  = {\mkern 1mu} {\mkern 1

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

$\int\limits_0^{\frac{\pi }{4}} {\sin {\mkern 1mu} {\mkern 1mu} 2x{\mkern 1mu} {\mkern 1mu} dx{\mkern 1mu} {\mkern 1mu}  = {\mkern 1mu} {\mkern 1mu} \left[ { - \frac{{\cos {\mkern 1mu} {\mkern 1mu} 2x}}{2}} \right]_0^{x/4}{\mkern 1mu} {\mkern 1mu} } $

$ = {\mkern 1mu} {\mkern 1mu}  - \frac{1}{2}\left( {\cos {\mkern 1mu} {\mkern 1mu} \frac{{2\pi }}{4}{\mkern 1mu} {\mkern 1mu}  - {\mkern 1mu} \cos {\mkern 1mu} 0} \right){\mkern 1mu} $

$ = {\mkern 1mu} {\mkern 1mu}  - \frac{1}{2}{\mkern 1mu} \left( {0 - 1} \right){\mkern 1mu} {\mkern 1mu}  = {\mkern 1mu} {\mkern 1mu} \frac{1}{2}$

$\int\limits_0^{\pi /4} {\sin \,\,2x\,\,dx}$ સદીશનું મૂલ્ય .... થાય .

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