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## Homework Statement

Evaluate ## \int \int \int_E {x}dV ## where E is enclosed by the planes ##z=0## and ##z=x+y+5## and by the cylinders ##x^2+y^2=4## and ##x^2+y^2=9##.

## Homework Equations

## \int \int \int_E {f(cos(\theta),sin(\theta),z)}dzdrd \theta ##

How do I type limits in for integration?

## The Attempt at a Solution

Right now I'm just trying to find the limits of integration.

For dz, ##z=x+y+5## is equivalent to ##z=rcos \theta +r sin \theta +5## so that is the upper limit for ##z## while ##z=0## is the lower limit.

For dθ I am going to assume that it is ##0 < \theta < 2 \pi ## By the way, how do I make the "greater than or equal to" sign in Latex? I choose zero and two pi because question didn't say the object is restricted to any octant. Keep in mind that I do not know what the graph looks like visually so I am taking a risk...

For dr, I have ##r^2 = 4## and ##r^2 = 9## what do I do? Additionally, can the lower limit for r ever be negative?