मराठी

For \[\int_0^{\frac\pi4}\sin^3 2t\cos 2t\,dt,\] which substitution and differential relation are correct?

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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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