Question

∫x√(a^2-x^2)dx

∫x√(a^2-x^2)dx 怎么求？？？

Answer 1

要从图像的角度来求，设y=√(a^2-x^2) 则 y≥0 将等号两边同平方 得
x^2 +y^2 =a^2 是个半圆（y≥0),∫x√(a^2-x^2)dx =∏×(a^2)÷2

Answer 2

∫x√(a^2-x^2)dx
=（1/2）∫√(a^2-x^2)dx^2
=-（1/2）∫(a^2-x^2)^(1/2)d(a^2-x^2)
=-（1/2)*1/[1+1/2]*(a^2-x^2)^(1+1/2)
=-(1/3)*(a^2-x^2)^(3/2)