高数二重积分,谢谢答:1、原式=∫(0,1)dx∫(0,x)√(x^2-y^2)dy =∫(0,1)dx*[(x^2/2)*arcsin(y/x)+(y/2)*√(x^2-y^2)]|(0,x)=∫(0,1)(π/4)*x^2dx =(π/12)*x^3|(0,1)=π/12 2、原式=∫(0,1)dy∫(0,√y)xy/√(1+y^3)dx =∫(0,1)dy*[(yx^2)/2√(1+y^3...
大一高数计算二重积分答:∴原式=∫(-1,0)dx∫(-x-1,x+1)(y-x)dy+∫(0,1)dx∫(x-1,1-x)(y+x)dy=…=4∫(0,1)x(1-x)dx= 2/3。(3)小题,D={(x,y)丨0≤x≤1,0≤y≤x}。∴原式=∫(0,1)xdx∫(0,x)sin(y/x)dy=(1-cos1) ∫(0,1)xdx=(1-cos1)/2。(4)小题,D={(x,y)...