∫∫（x²-y²）dσ
=∫[0,π]∫[0,sinx]（x²-y²）dydx
=∫[0,π]（x²y-y^3/3）[0,sinx]dx
=∫[0,π]（x^2sinx-sinx^3/3）dx
=∫[0,π]x^2sinxdx-∫[0,π]sinx^3/3dx
=-∫[0,π]x^2dcosx+∫[0,π](1-cos^2 x)/3dcosx
=-x^2cosx[0,π]+2∫[0,π]xcosxdx+(cosx-cos^3x /3)/3[0,π]
=π^2+2∫[0,π]xdsinx-2/9-2/9
=π^2-4/9+2∫[0,π]xdsinx
=π^2-4/9+2xsinx[0,π]-2∫[0,π]sinxdx
=π^2-4/9+2cosx[0,π]
=π^2-4/9-4
=π^2-40/9