Question

How do i do this???

Let R be the region in the xy-plane between the graphs of y = ex and y = e-x from x = 0 to x = 2.

a) Find the volume of the solid generated when R is revolved about the x-axis.

Answer 1

did you graph the functions?

Answer 2

no, what exactly do i graph?

Answer 3

y=e^x , y=e^-x, and x=2

Answer 4

ok then what?

Answer 5

then you're taking the region and rotate it over the x axis - try to get the 3d shape

Answer 6

you'll have to use the washer method

Answer 7

Í (πR^2 - πr^2) dx , from 0 to 2

Answer 8

ok thank you I see, then what?

Answer 9

what is R and what is r?

Answer 10

so R and r would be from top to bottom or left to right?

Answer 11

imagine a quarter with a whole in the middle (washer) positioned vertically so you can stack all these washers to approximate the volume.... R is from the x axis to y=e^x, and r is from the x axis to y = e^-x