Question

请教各位学霸这道高等数学积分题怎么做？就是中间这道题

非常感谢

Answer 1

令 x = sint
I = ∫<0, π/2>sintcostdt/{[2-(sint)^2]cost}
= ∫<0, π/2>sintdt/[2-(sint)^2] = -∫<0, π/2>dcost/[1+(cost)^2]
= -[arctan(cost)]<0, π/2> = π/4

Answer 2

可以尝试三角代换。