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Don't know where to start on calculus III integral?
Integrate the function f(x,y,z)=2x+y over the solid between the planes z=0 and z =3, contained between cylinders of radii sqrt(50) and sqrt(98) (centered on the z axis), and restricted to the half-space y<x
1 Answer
- Barry GLv 76 years ago
f(x,y,z) does not depend on z. So integrate over the specified region R in the xy plane. Then multiply by 3. The integral can be done more easily using polar co-ordinates : x = rcosθ, y = rsinθ. The element of area becomes
dA = dx dy = r dr dθ.
The limits are r^2=50 to 98 and θ=π/4 to 5π/4.
