Solution
= Solution
The double-angle identity gives $\cos^2x-\sin^2x=\cos(2x)$. Thus
$$
\boxed{\int_0^\pi(\cos^2x-\sin^2x)dx=\left[\tfrac12\sin(2x)\right]_0^\pi=0.}
$$
= Solution
The double-angle identity gives $\cos^2x-\sin^2x=\cos(2x)$. Thus
$$
\boxed{\int_0^\pi(\cos^2x-\sin^2x)dx=\left[\tfrac12\sin(2x)\right]_0^\pi=0.}
$$