anonymous
  • anonymous
Can anyone prove the volume of an ellipse?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Do you mean find an area or actually prove the formula?
anonymous
  • anonymous
LOL can u read it?
dumbcow
  • dumbcow
yeah i can zoom in. so basically they want you to use calculus to derive the formula for volume of a 3-d ellipse

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anonymous
  • anonymous
yes :D
dumbcow
  • dumbcow
ok, start with equation of ellipse: \[\frac{x^{2}}{b^{2}} +\frac{y^{2}}{a^{2}} = 1\] |dw:1327556444323:dw| then integrate from -b to b, of A(x) which is the area of each circular cross-section where the radius is y: solve the ellipse equation for y \[y = \sqrt{a^{2} - \frac{a^{2}}{b^{2}}x^{2}} = \frac{a}{b}\sqrt{b^{2}-x^{2}}\]
anonymous
  • anonymous
Thanks for ur help :D That was awesome and very clear
anonymous
  • anonymous
wait how did u get that equation
dumbcow
  • dumbcow
which one?
anonymous
  • anonymous
like from the first to the second
anonymous
  • anonymous
ohhh i get it now
anonymous
  • anonymous
but do i have to integrate it?
anonymous
  • anonymous
or is this the end result?
dumbcow
  • dumbcow
sorry i skipped some simplifying steps.. no you still have to integrate \[V = \pi \int\limits_{-b}^{b}y^{2} dx\] plug that equation in for y
anonymous
  • anonymous
huh i doubt i will be able to integrate that on my own
dumbcow
  • dumbcow
ok \[y^{2} = \frac{a^{2}}{b^{2}}(b^{2}-x^{2})\] factor out the constants \[V = \frac{a^{2} \pi}{b^{2}}\int\limits_{-b}^{b} (b^{2} -x^{2}) dx\]
anonymous
  • anonymous
|dw:1327557477105:dw|
dumbcow
  • dumbcow
yep :)
anonymous
  • anonymous
|dw:1327557564379:dw|
anonymous
  • anonymous
Is that correct?
dumbcow
  • dumbcow
not quite, you skipped a step first evaluate from -b to b by plugging them in for x
dumbcow
  • dumbcow
we don't want x in our answer
anonymous
  • anonymous
oh ya whoops lol
anonymous
  • anonymous
|dw:1327557858057:dw|
anonymous
  • anonymous
|dw:1327557996710:dw|
anonymous
  • anonymous
This shld be the answer :D
dumbcow
  • dumbcow
looks good :) don;t forget about the pi
anonymous
  • anonymous
oh yes thanks for ur help and patience
dumbcow
  • dumbcow
this is the same way of finding volume of sphere as well just make a =b
anonymous
  • anonymous
ok thanks :D
anonymous
  • anonymous
Goodnight

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