Finding the Area/Volume of a solid using the shell/disk/washer method..
Ive been working on this problem for a while, and I can't get very far with it. I don't really know what to do.
Let R be the region bounded by the graphs of y=√x, y=e^-x and the y axis.
a) Find the area of R
b) Find the volume of the solid generated when R is revolved about the horizontal line y=-1
c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a semi circle whose diameter runs from the graph y=√x to the graph of y=e^-x. Find the volume of the solid.
For A, I think Im supposed to used the formula A=bh. And becasue of the way the graph looks I think its supposed to be A=(√x)(e^-x). But I don't really know where to go from there.
For B, I think I'm supposed to use the formula v=∫2πrh dx
And for C, I don't really have any idea. From looking at my notes, I have the area formula of a semi-circle, which is A=πd^2/8...