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Question
Which function is an antiderivative of \[\sin^3 2t\cos 2t?\]
Options
\[F(t)=\frac14\sin^4 2t\]
\[F(t)=\frac18\sin^4 2t\]
\[F(t)=\frac18\sin^3 2t\]
\[F(t)=\frac12\sin^4 2t\]
MCQ
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Solution
The substitution gives \(\frac12\int u^3\,du=\frac18u^4\).
Replacing \(u\) by \(\sin 2t\) yields \(F(t)=\frac18\sin^4 2t\).
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