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प्रश्न
For \[\int_0^{\frac\pi4}\sin^3 2t\cos 2t\,dt,\] which substitution and differential relation are correct?
पर्याय
\[\sin 2t=u,\qquad \cos 2t\,dt=\frac12\,du\]
\[\sin^3 2t=u,\qquad \cos 2t\,dt=du\]
\[\cos 2t=u,\qquad \cos 2t\,dt=2\,du\]
\[2t=u,\qquad \cos 2t\,dt=\frac12\,du\]
MCQ
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उत्तर
Put \(\sin 2t=u\), so that \(2\cos 2t\,dt=du\).
Therefore \(\cos 2t\,dt=\frac12\,du\), and the integral becomes \(\frac12\int u^3\,du\).
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