Question

Prove that \(\int_0^\pi\frac{xdx}{a^2cos^2x + b^2sin^2x}\) = π²/2ab

Answer 1

  \(\int_0^\pi\frac{xdx}{a^2cos^2x + b^2sin^2x}\) 

(Dividing number and denoted. by cos²x)

where, let tanx = t ⇒ sec²xdx = dt

if x = 0, then t = 0,