# Thread: setting up integral (volume)

1. ## setting up integral (volume)

Find the volume of the following solid, bounded by the surfaces:

z = x + e^y,
z = 0,
y = x^2 + 1
and x + y = 3

Note* just set up the integral, do not evaluate

2. Originally Posted by boousaf
Find the volume of the following solid, bounded by the surfaces:

z = x + e^y,
z = 0,
y = x^2 + 1
and x + y = 3

Note* just set up the integral, do not evaluate
Have you drawn a rough sketch?

More than one correct answer is possible. Here's one such:

$V = \int_{x=a}^{x=b} \int_{y=x^2 + 1}^{y=-x+3} \int_{z=0}^{z = x + e^y} dz \, dy\, dx$

where a and b are the x-coordinates of the intersection points of $y=x^2 + 1$ and y = -x + 3.

3. thanks mr fantastic! very helpful