Use the shell method to find the volume between y=e^x , y=e^-x nad x=1 about the y -axis

Question

anonymous · Answer

i got 4,623 as my answer. i can walk you through what i did if my answer is wrong

anonymous · Answer

anyone?

phi · Answer

the set-up should be
$$ 2 \pi \int_0^1 (e^x - e^{-x}) x \ dx $$

anonymous · Answer

i've got that, i then split it into 2 integrals; Sxe^x-Sxe^-x and used integration by parts to solve

phi · Answer

yes.  sounds correct.

anonymous · Answer

this left me with $$2\pi[(x e^{x}-e^{x})-(xe^{-x}-e^{-x})]$$ from 0 to 1

phi · Answer

I get
$$ 2\pi[(x e^{x}-e^{x})-(-xe^{-x}-e^{-x}) ]\bigg|_0^1 $$

anonymous · Answer

looks like i forgot to type the -, i got the same

phi · Answer

the final answer is 4 pi / e

anonymous · Answer

i didnt write it in that form, but i got the same 4.623

phi · Answer

yes.  But it is probably best to write it in exact form.  Then the final decimal version can be rounded to the appropriate precision, depending on how it is being used.  Also, 4 pi /e
looks nicer

anonymous · Answer

will do, thanks!