Here is the problem.
Let S be the region in the first quadrant bounded by the graphs of y=e^(-x^2) , y=2x^2, and the y- axis
a. Find the area of the region S
b. Find the volume of the solid generated when the region S is rotated about the x axis
c. The region s is the base of a soid for which each cross section perpendicular to the x-axis is a semi-circle with diameter in the xy plane. Find the volume of this solid.
The Attempt at a Solution
I don't really have any idea how to solve this problem. I understand the process using normal functions however the e is putting me at a loss. I am trying to do it by hand so I can understand it, but am completely lost.
Heres what I've done. Since e is base of ln.
lny= -x^2 ln e = lny=-x^2 Therefore x= sqrt(-lny)
With the other equation in terms of x as I am asuming I am solving for it about the y-axis for part a. x = sqrt(y/2)
From here I get confused, I don't know how to graph x=sqrt(-lny)
I can't figure out how to find the bounderies of the interval so I can't find the area or the volume. Any help would be appreciated.:uhh: