早教吧作业答案频道 -->数学-->
∫√(4-x^2)/x^2∫√(4-x^2)/x^2dx
题目详情
∫√(4-x^2)/x^2
∫√(4-x^2)/x^2dx
∫√(4-x^2)/x^2dx
▼优质解答
答案和解析
设x=2siny,则y=arcsin(x/2),coty=√(4-x²)/x,dx=2cosydy
故 原式=∫2cosy*2cosydy/(4sin²y)
=∫cos²ydy/sin²y
=∫cot²ydy
=∫(csc²t-1)dy
=C-coty-y (C是积分常数)
=C-√(4-x²)/x-arcsin(x/2).
故 原式=∫2cosy*2cosydy/(4sin²y)
=∫cos²ydy/sin²y
=∫cot²ydy
=∫(csc²t-1)dy
=C-coty-y (C是积分常数)
=C-√(4-x²)/x-arcsin(x/2).
看了 ∫√(4-x^2)/x^2∫...的网友还看了以下：