计算由三个坐标面与平面x=4，y=4及z=x2+y2+1所围立体的体积．
V=∫04dx∫04dy ∫0x2+y2+1dz=∫04dx∫04(x2+y2+1)dy =∫04[y+x2y+(1/3)y3∣04)dx =∫04[4+4x2+64/3)dx=(76/3)x+(4/3)x3∣04 =76×4/3+4×64/3=560/3
计算由三个坐标面与平面x=4，y=4及z=x2+y2+1所围立体的体积．
V=∫04dx∫04dy ∫0x2+y2+1dz=∫04dx∫04(x2+y2+1)dy =∫04[y+x2y+(1/3)y3∣04)dx =∫04[4+4x2+64/3)dx=(76/3)x+(4/3)x3∣04 =76×4/3+4×64/3=560/3
