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3-1.Vectors
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$\int\limits_0^{\pi /4} {\sin \,\,2x\,\,dx}$ સદીશનું મૂલ્ય .... થાય .
A
$\frac{1}{x}$
B
$1$
C
$0$
D
$\frac{1}{2}$
Solution
$\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}$
Standard 11
Physics
