Solve Ellipsoid Problem: Integrate cos(theta)*sqrt[cos^2(theta) - (x^2/a^2)]

[Yura]

Homework Statement

someone asked the ellipsiod problem before and i didnt under stand anythign in the repsonces >< but i had already gotten this far that my equation (simplified) is

cos(theta)*sqrt[cos^2(theta) - (x^2)/(a^2)]

i need to integrate this equation with respect to d(theta)

or even just this part: sqrt[cos^2(theta) - (x^2)/(a^2)]
(if intergration by parts is required)

Homework Equations

The Attempt at a Solution

i tried using by parts but i ended up with a lot of numbers getting more and more complex

i at least need to know if by using integration by parts is heading in the right direction for this
and if it is, then which values do i set for the v' and u?

i've tried both ways but neither seems to be gettig me anywhere, I've had to do so many different intergrations by part for each because there are more within each one.


or is there some rule that i should be using to solve for this intergration?

thanks in advance

 

[HallsofIvy]

Homework Statement

someone asked the ellipsiod problem before and i didnt under stand anythign in the repsonces >< but i had already gotten this far that my equation (simplified) is

cos(theta)*sqrt[cos^2(theta) - (x^2)/(a^2)]

i need to integrate this equation with respect to d(theta)

or even just this part: sqrt[cos^2(theta) - (x^2)/(a^2)]
(if intergration by parts is required)

I cannot imagine why integration by parts would be required- it's an easy substitution: replace cos^2(theta) with 1- sin^2(theta) and then let v= sin(theta)

Homework Equations

The Attempt at a Solution

i tried using by parts but i ended up with a lot of numbers getting more and more complex

i at least need to know if by using integration by parts is heading in the right direction for this
and if it is, then which values do i set for the v' and u?

i've tried both ways but neither seems to be gettig me anywhere, I've had to do so many different intergrations by part for each because there are more within each one.


or is there some rule that i should be using to solve for this intergration?

thanks in advance