Question

Find the volume of the solid formed when the graph of the region bounded by y=e^x , y=1 and x=4 is revolved about the x-axis (please show work)

Answer 1

Love calc II. \[\int\limits_{0}^{4}Cross Sectional Area\]
I solved x for y=1 which gets x=0 to the given x=4
The cross sectional area is a circle so: pi r^2
the r = e^x
so the cross sectional area = pi e^2x
so \[\pi \int\limits_{0}^{4}e ^{2x}\]

Answer 2

okay, thanks!

Answer 3

I got pi(1/2)(e^8-1).

Answer 4

I used the same arithmetic as you and received the same expression, yet when i solve it by hand i get the answer of 548.3.........yet when i plug in the integral in my ti-84 i get 4680.9.......... i do not understand why there is a difference :/