换元法求∫（a^2-x^2)^1/2dx
问题描述：
换元法求∫（a^2-x^2)^1/2dx
答
令x=asint dx=acostdt t=arcsin(x/a)
原式=∫a^2cos^2tdt
=a^2/2*∫(1+cos2t)dt
=a^2/2*(t+sintcost)+C
=a^2/2*arcsin(x/a)+ax/2*(1-x^2/a^2)^(1/2)+C