计算定积分 $\displaystyle\int_{0}^{\frac{\pi}{2}}\ln(a^2\cos^2 x+b^2\sin^2 x)\cos 2m x\mathrm{d}x$.
计算定积分
\[\int_{0}^{\frac{\pi}{2}}\ln(a^2\cos^2 x+b^2\sin^2 x)\cos 2m x\mathrm{d}x.\]
Answer
计算定积分
\[\int_{0}^{\frac{\pi}{2}}\ln(a^2\cos^2 x+b^2\sin^2 x)\cos 2m x\mathrm{d}x.\]