Question

find the volume enclosed by x²+y²=4 and z=x+4y using multiple integrals?

Answer 1

I think you need more information like z = 0 ( so it can be above the xy plane )

Answer 2

Then find the area only in first ocatne

Answer 3

\[\int\limits_{0}^{\pi/2}\int\limits_{0}^{2}\int\limits_{0}^{r \cos \theta+4r \sin \theta}rdzdrd \theta\]

Answer 4

you should use cyindrical because the region in the xy plane is circular in nature
you have to convert the z bounds then the low z bound is z = 0 and the high z bound is z = x + 4y
you said only the first octant so after the z integration you are down to the quarter circle in the first quadrant which has
r bounds r = 0 to r = 2 (the circle of radius 2 centered at the origin)
theta bounds of theta = o to theta = Pi/2

Answer 5

Well that is quite right. I find difficulty in drawing graph in 3d through and then finding it's limit. Any guess.