求反常积分 ∫[0,+∞] (sinax/x)^2dx

Question

求反常积分 ∫[0,+∞] (sinax/x)^2dx

Answer 1

\int_0^{+\infty}\left(\frac{\sinax}{x}\right)^2dx
做变换u=ax
=a*\int_0^{+\infty}\left(\frac{\sinu}{u}\right)^2du
=a*\frac{\pi}{2}