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:
$\displaystyle V = \int_{x=a}^{x=b} \int_{y=x^2 + 1}^{y=-x+3} \int_{z=0}^{z = x + e^y} dz \, dy\, dx$
where a and b are the x-coordinates of the intersection points of $\displaystyle y=x^2 + 1$ and y = -x + 3.