Question

对根号下1-x的平方,积分,区域为0到1 为什么答案是4分之派

Answer 1

令x=sint,则t∈[0,π/2],dx=costdt
∫【0→1】√(1-x²)dx
=∫【0→π/2】cost ·costdt
=∫【0→π/2】cos²tdt
=∫【0→π/2】(1+cos2t)/2dt
=[t/2+(sin2t)/4]【0→π/2】
=π/4+0-0-0
=π/4
答案：π/4