# # 3D # (%i10) integrate(1, y,-sqrt(r^2-x^2-y^2), sqrt(r^2-x^2-y^2)); (%i11) integrate(%,y,-sqrt(r^2-x^2),sqrt(r^2-x^2)); (%i12) integrate(%,x,-r,r);
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# # 4D # (%i13) integrate(2*sqrt(r^2-x1^2-x2^2-x3^2), x1, -sqrt(r^2-x2^2-x3^2), sqrt(r^2-x2^2-x3^2)); (%i14) integrate(%, x2, -sqrt(r^2-x3^2), sqrt(r^2-x3^2)); (%i15) integrate(%, x3, -sqrt(r^2), sqrt(r^2));
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# # 5D # (%i20) integrate(2*sqrt(r^2-x1^2-x2^2-x3^2-x4^2), x1, -sqrt(r^2-x2^2-x3^2-x4^2), sqrt(r^2-x2^2-x3^2-x4^2)); (%i21) integrate(%, x2, -sqrt(r^2-x3^2-x4^2), sqrt(r^2-x3^2-x4^2)); (%i22) integrate(%, x3, -sqrt(r^2-x4^2), sqrt(r^2-x4^2)); (%i23) integrate(%, x4, -r, r);
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