Solution
= Solution
The product-to-sum identity for the <sine> gives $\sin2x\sin4x=\frac12(\cos2x-\cos6x)$. Each <cosine> has zero <integral> on this interval, so
$$
\boxed{I=0.}
$$
This is also an instance of <Fourier orthogonality>.
= Solution
The product-to-sum identity for the <sine> gives $\sin2x\sin4x=\frac12(\cos2x-\cos6x)$. Each <cosine> has zero <integral> on this interval, so
$$
\boxed{I=0.}
$$
This is also an instance of <Fourier orthogonality>.