# Evaluate the following triple integral

## Homework Statement

Evaluate the following triple integral

$$I = \int\int\int_{R}x dv$$

in Cartesian coordinates where R is the finite region bounded by the surfaces z=0, y=x^3, y=8, z=x. Sketch the region R. Here dV is the element of volume.

## The Attempt at a Solution

What I'm having trouble with is setting up the limits of integration.

0 < z < x
x^3 < y < 8

And how do I know that the y and z limits are that way around and not x < z < 0 and 8 < y < x^3 instead?

HallsofIvy