∫（0,1）根号下[1-x^2]dx=
问题描述：
∫（0,1）根号下[1-x^2]dx=
答
令x=sint ,dx=costdt 当x=0时,t=0,当x=1时,t=π/2∫（0,1）根号下[1-x^2]dx= ∫(0,π/2)√(1-sin²t)costdt= ∫(0,π/2)√(1-sin²t)costdt=∫(0,π/2)cos²tdt =∫(0,π/2) [(cos2t +1)/2]dt=1/2∫(0,...