2 different ways to change the drag on a plane?

Integral - Volume under a plane and over xy-plane?

• Compute the volume of the region under the plane z=8x+6y+32 and over the region in the xy-plane bounded by the circle x^2+y^2=6y Hint: There are two ways of doing this problem. First method: Change variables translationally X=x, Y=y−3 to bring the centre of the circle to the origin and then use polar coordinates in the new variables. Second method: Use polars directly. Here you'll have to figure the polar equation of the circle and also the appropriate range of Teta.

• Answer:

  I am typing in my iPod, so I can't give you full detail answer. But I will give you all theism formation you need. I will use change of variable method, X=x, Y=y−3. Note that dV in XY is the same as dV in XY-plane that is, the jocobian factor is 1 So the triple integral will have limits: 0<= theta <= 2pi, 0<= r<=3, the cire has radius 3. 0<=z<=8cos(theta)+6sin(theta)+32 Additional: The integrand is only dV since jacobian is 1