Question

Evaluate \[\int_0^{\frac\pi4}\sin^3 2t\cos 2t\,dt.\]

Options

• \[\frac18\]

• \[\frac14\]

• \[0\]

• \[\frac\pi4\]

Answer 1

Use \(F(t)=\frac18\sin^4 2t\) and compute \(F\left(\frac\pi4\right)-F(0)\).
Since \(\sin\frac\pi2=1\) and \(\sin0=0\), the value is \(\frac18\).