f(x)=sqrt(4-x^2)的原函数怎么求

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f(x)=sqrt(4-x^2)的原函数怎么求f(x)=sqrt(4-x^2)的原函数怎么求f(x)=sqrt(4-x^2)的原函数怎么求令x=2cost(0≤t则sqrt(4-x^2)dx=sqrt

f(x)=sqrt(4-x^2)的原函数怎么求
f(x)=sqrt(4-x^2)的原函数怎么求

f(x)=sqrt(4-x^2)的原函数怎么求
令x = 2cost(0≤t则sqrt(4-x^2) dx = sqrt[4-4(cost)^2] = sqrt[(4sint)^2] = 2sint(0≤tdx = d(2cost) = -2sint dt
所以f(x) dx = -4(sint)^2 dt
积分,将t换回x可得f(x)的原函数