1. ## Area/Volume between Curves

I'm trying to help my sister out with a calc problem that she has in her study guide, and I no longer remember how to do these. Any help is appreciated (and i'm doing this somewhat off memory)

There are two curves in question: y = 3^x+1 , and y = 5-2x^2
Region M is defined below 3^x+1 and to the left of 5-2x^2, also bounded by x=0 and y=0.
Region N is defined as the section between the two curves.

1. Find the area of M and N.
2. Find the volume of the solid generated when the region N is rotated about the x-axis.

Thank you

2. What's the first curve? $\displaystyle y = 3^{x+1}$ or $\displaystyle y = 3^{x}+1$?

In either case, you will need to find the points of intersection. This may not be a particularly trivial task.

I'm not quite sure what "to the left of" means. Maybe a short quiz will help.

Is the point (0.2,4) in the shaded region?
Is the point (0.4,3) in the shaded region?
Is the point (0.6,2) in the shaded region?

3. I think, you made a typo in the equation of the first curve, and it should be $\displaystyle \mathsf{y=3x+1}$