y=lnx和y=(e+1)-x的交点为(e,1)
分成两个积分:
I=∫∫(D)√xdxdy
=∫(1,e)√xdx∫(0,lnx)dy+ ∫(e,e+1)√xdx∫(0,e+1-x)dy
=∫(1,e)lnx√xdx+∫(e,e+1)√x(e+1-x)dx
=(2/9)x^(3/2)(3lnx-2)|(1,e)+ [(e+1)(2/3)x^(3/2)-(2/5)(x^(5/2)]|(e,e+1)
=(2/9)(e^(3/2)+2)+(4/15)(e+1)^(5/2)-[(e+1)(2/3)e^(3/2)-(2/5)(e^(5/2)]
自己再化简下