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प्रश्न
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
पर्याय
\[-\int(1-t^2)t^2\,dt\]
\[-\int(1+t^2)t^2\,dt\]
\[\int(1-t^2)t^2\,dt\]
\[\int(1-t^2)t\,dt\]
MCQ
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उत्तर
Using \[\sin^2x=1-\cos^2x\] gives \[1-t^2\]. Also, \[\cos^2x=t^2\] and \[\sin x\,dx=-dt\].
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