高数二重积分，谢谢
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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)]|(0,√y)
=(1/2)*∫(0,1)(y^2)/√(1+y^3)dy
=(1/6)*∫(0,1)d(1+y^3)/√(1+y^3)
=(1/3)*√(1+y^3)|(0,1)
=(√2-1)/3
=∫(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)]|(0,√y)
=(1/2)*∫(0,1)(y^2)/√(1+y^3)dy
=(1/6)*∫(0,1)d(1+y^3)/√(1+y^3)
=(1/3)*√(1+y^3)|(0,1)
=(√2-1)/3
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