Question

积分题，谢谢

let x=2-cosθ。∫（下面是1.5，上面是2）（x-1除以3-x）二分之一次方dx

Answer 1

x=2-cosθ dx=sinθdθ
∫√(x-1)/(3-x)dx x积分区间[1.5,2]
=∫√((1-cosθ)/1+cosθ))sinθdθ
=∫((1-cosθ)/sinθ)sinθdθ
=∫(1-cosθ)dθ
=θ+sinθ -------x=2-cosθ x积分区间[1.5,2] ,θ积分区间为[π/3,π/2]
=1+π/6-√3/2