Question

its a integration question
find the volume of ellipsoid by rotating the ellipse
x^2/a^2 + y^2/b^2=1

Answer 1

\[x^2/a^2+ y^2/b^2 =1\]

Answer 2

On rotating the ellipse around the x-axis, an ellipsoid is formed.
Consider a thin cylinder of thickness dx at a distance of x from the origin whose radius = y
Volume of this thin cylinder,
dV = πy^2 dx
=> Volume of the ellipsoid, V
= ∫ (x = - a to x = a) dV
= ∫ (x = - a to x = a) πy^2 dx
= ∫ (x = - a to x = a) π * (b^2/a^2) (a^2 - x^2) dx
= (πb^2/a^2) [a^2x - x^3/3] ... [x = - a to x = a]
= (πb^2/a^2) [(a^3 - a^3/3) - (- a^3 + a^3/3)]
= (πb^2/a^2) * (4/3) a^3
= (4/3) πab^2.

Answer 3

whoa thanks
you solved the whole problem :D

Answer 4

np :)

Answer 5

Man that is painful on my eyes. I need latex.

Answer 6

Since I take it you're all new.
You can make mathematical text look nice using \(LaTeX...\)
\(\large \frac{x^2}{a^2} + \frac {y^2}{b^2}= 1\)
Code for that:
```
\(\large \frac{x^2}{a^2} + \frac {y^2}{b^2}= 1\)
```
So basically if you want math text to look nice input it in between.
\(\(\) and \)

Answer 7

How do you add code!!?

Answer 8

help me with the diagram though :|

Answer 9

add code using `
like
\(` aa `\)
will give you `aa`

Answer 10

For inline math use `\(` and `\)`. For full math use `\[` and `\]`

Answer 11

-_-

Answer 12

we are deviating from the question!!
someone help him with the diagram!

Answer 13

are you suree???

Answer 14

there is no area bounded by them,so volume either

Answer 15

` | へ　　へ　 `
` | の の \\ `
` | も `
` | へ | `
` \__________/ `

Answer 16

cute

Answer 17

On rotating the ellipse around the x-axis, an ellipsoid is formed.
Consider a thin cylinder of thickness dx at a distance of x from the origin whose radius = y
Volume of this thin cylinder,
\(dV = \pi y^2 dx\)
=> Volume of the ellipsoid, V
\(\Large= ∫ (x = - a\) to \(x = a) dV\)
\(\Large= ∫ (x = - a\) to x = a) \(\pi y^2 dx\)
\(\Large= ∫ (x = - a\) to \(x = a) \pi * (\frac{b^2}{a^2}) (a^2 - x^2) dx\)
\(\Large= (\frac{\pi b^2}{a^2}) [a^2x - \frac{x^3}{3}]\) ... \([x = - a\) to \(x = a]\)
\(\Large= (\frac{\pi b^2}{a^2}) [(a^3 - \frac{a^3}{3}) - (- a^3 + \frac{a^3}{3})]\)
\(\Large= (\frac{\pi b^2}{a^2}) * (\frac{4}{3}) a^3\)
\(\Large= (\frac{4}{3}) \pi ab^2.\)

@wio \(LaTeX!\)

Answer 18

∫(x=−a to x=a)dV
should be
\[ \int_{-a}^adV \]
`\[ \int_{-a}^adV \]`

Answer 19

how about
\[ \int \limits _{-a}^adV \]
`\[ \int \limits _{-a}^adV \]`