Integrate the function f(xyz)=−6x+5y over the solid given by the figure below, if P=(-6,-6,3), Q=(-3,-3,3), R=(3,3,3), and S=(6,6,3). (The figure is based on the xy-plane.) the figure seems to be touching or on the xy plane.
i don't know how to paste the picture but it's basically taking the bigger cylinder and subtracting it from the small cylinder to get a thin hollowed cylinder
so i know that in order to find the range for the angles you need to take the tan() of the x and y: tan(theta)=-6/6, theta=5pi/4 tan(theta)=3/3 theta=pi/4
the radius is just sqrt(3^2 + 3^2)=sqrt(18) and sqrt(6^2 + 6^2)=sqrt(72)
so my triple integral would be:
integral(theta=pi/4 to theta=5pi/4) of integral(r=sqrt(18) to r=sqrt(72)) of integra(0 to 3) of -6x+5y...
i've tried 5 times and i got the answer wrong. I need help!!