Question

Rotating the function y= e^(-0.5x) about the x-axis on the interval [-1, 0] yields a solid of revolution with a volume of?

Answer 1

what have you drawn out so far?

Answer 2

well i dont know how to find the integral of that function

Answer 3

of what function? what have you worked out so far?

Answer 4

the function y= e^(-0.5x)... i need\[:\pi \int\limits\limits_{-1}^{0} y^2\]

Answer 5

looks good so far

(e^-.5x)^2 is equal to what?

Answer 6

this turns out to be a pretty elementary function after all

Answer 7

e^-1x

Answer 8

correct

Answer 9

and if you want to, we can turn this about and get the same results from:\[pi\int_{0}^{1}e^x dx\]

Answer 10

lets just try and stick with the original equation, dont want to confuse me ;)

Answer 11

:) k

Answer 12

so is it like pi(e^0-e^-1)

Answer 13

almost

lets work the integration and see if we get a good setup to play with

Answer 14

e^-x comes from something akin to e^-x to begin with; but its missing something

Answer 15

can you do a usubstitution on it? if you really really need to?

Answer 16

i'm not sure what you mean.. we already have the integral dont we?

Answer 17

i dont think your setup as correct. id feel better if we stepped thru it to be sure tho

Answer 18

okay, lets go step by step

Answer 19

give me your integration of e^-x

Answer 20

-e^-x

Answer 21

that looks better; now piece it all in:

pi[-e^0-(-e^-1)]

pi(-1-(-1/e))

Answer 22

thats alot of negatives. lol

Answer 23

:) we can clean it up if need be

Answer 24

lets do that

Answer 25

-pi(1-(1/e))

-pi(e-1)/e

Answer 26

ugh, i think i misplaced a negative along the way

Answer 27

answers are:
A. pi(e+1)
B. pi(e^2-1)
C. pi(e-1)
D. pi(e^2+1)

Answer 28

-e^-0 - -e^--1 lol

Answer 29

pi(-1 + e)

Answer 30

looks like c is our best match

Answer 31

okay, thats what i think too. thanks for your help. can i ask you another one?

Answer 32

dunno, i think i used up all my mojo sorting that one out :/

Answer 33

haha well thanks anyways!

Answer 34

good luck ;) just post a new question to the left after you close this one out and someones bound to bite