Question

GIVING MEDAL TO FIRST ANSWER AND FANNING IMMEDIATELY. calculate the volume obtained when the area bounded by y=e^x, x=1, y=1, is rotated around x=4. use shell method. Can I see your integral?

Answer 1

my integral is this but it is wrong :
¨
integral of 2pi(4-x)(e^x-1) dx from 0 to 1

Answer 2

@bahrom7893 what are u thinking about?

Answer 3

@hartnn @halorazer @mathslover @ganeshie8

Answer 4

integral of pi((4-lnx)^2-9) FROM 1 to e =/= integral of 2pi(4-x)(e^x-1) dx from 0 to 1!!!

Answer 5

I do not understand why! My teacher said the first one (with the ln()) is good. But, I do not see why the second integral does not give the same answer.

Answer 6

tkhunny, any lead?

Answer 7

@tkhunny any lead?

Answer 8

Is anyone working on this? haha I feel desperate waiting here...

Answer 9

I usually do these both ways UNTIL I get the same answer.

Shells (Reference \(2\pi rh\;dr\))
\(2\pi\int\limits_{0}^{1}(4-x)(y-1)\;dx = 2\pi\int\limits_{0}^{1}(4-x)(e^{x}-1)\;dx = \)

Disks (Reference \(\pi r^{2}\;dh\))
\(\pi\int\limits_{1}^{e}(4-x)^{2}\;dy - \pi 3^{2}(e-1) = \pi\int\limits_{1}^{e}(4-\ln(y))^{2}\;dy - 9\pi(e-1) = \)

Seems right. If they are not the same answer, you just have to stare at it long enough to see the error.

Answer 10

hmmm

Answer 11

http://www.wolframalpha.com/input/?i=integral+of+pi%28%284-lnx%29%5E2-9%29+FROM+1+to+e

Answer 12

http://www.wolframalpha.com/input/?i=integral+of+2pi%284-x%29%28e%5Ex-1%29+from+0+to+1

Answer 13

they do not give the same answer!

Answer 14

Are you sure? It is not always obvious.

Answer 15

look at wolfram alpha websites, they give different numerical value.

Answer 16

Okay, your task is to find out why? What error is there in what seemed to be an obvious setup? It is definitely NOT always obvious. Something is missing. What is it?

For starters, one of the Wolfram results is not correct. This is an excellent reminder that we should not trust without judgment. Where did the \(\pi\) go?

Answer 17

one setup is using shells, the other is using washers

Answer 18

no my job is not to find why they are wrong. I just happened to try out both methods. But i get different results.

Answer 19

I know my teacher approves the one with the ln(). I dont get why the other one is wrong.

Answer 20

Nonresponsive. How do you plan to deal with the incorrect Wolfram result?

I forced it... http://www.wolframalpha.com/input/?i=%28integral+of+%284-x%29%28e^x-1%29+from+0+to+1%29*2*pi

Answer 21

OHHHHHHHH

Answer 22

TKHUNNY YOU MUST HAVE A POSTDOCTORAL PHD

Answer 23

You just have to pay attention. Trust but verify. Software is great, but so far, humans still have to think!!

I'm guessing it's an input error of some sort. There is no substitute for knowing what you are doing. Trusting the machine is almost never a good idea.

Answer 24

I dont understand why wolfram messes up.... It's the first time this happens... There must be something going on that we don't understand... By the way, what level are you?