Discussion
\(\int \frac{\sin 4\theta}{\sin 2\theta}d\theta =\)
Answer: E
The integral is \(\sin 2\theta + C\).
Since \(\sin 4\theta = 2\sin 2\theta\cos 2\theta\), the integrand is \(2\cos 2\theta\):
\[ \int 2\cos 2\theta\,d\theta = \sin 2\theta + C \]
\(2\sin 2\theta\) forgets to divide by the 2 from the chain rule, \(\cos 2\theta\) is a derivative of the wrong kind, and the options in \(\sin\theta\) or \(\cos\theta\) do not differentiate back to \(2\cos 2\theta\).
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