How can I solve a volume integral question with a trig substitution?

[ppy]

Hi,

I was attempting a volume integral question out of a book. I know what the final answer is and what integral i am supposed to work out but I do not know how I am supposed to solve it. I have tried different ways such as integration by substitution and integration by parts but I do not seem to be getting anywhere.

This is the ∫^{1}_{-1} 4(√(1-x^{2}))(x+1)dx The answer is 2pi.

any help would be great thanks.

 

[davidmoore63@y]

This is not a volume integral. Put x=sin u and proceed

 

[ppy]

The integral started out as a triple volume integral. The part mentioned is the final part of the triple integral. I have tried x=sinu and still got nowhere. Is it a simple substitution or do I have to integrate by parts as well ?
Thanks

 

[tiny-tim]

hi ppy!

I have tried x=sinu and still got nowhere. Is it a simple substitution or do I have to integrate by parts as well ?

davidmoore63@y's substitution does work …

show us how far you got with it ​

 

[ppy]

Thanks. I've got there now !

 

[Mark44]

The presence of the $\sqrt{1 - x^2}$ factor suggests that a trig substitution is called for, and that's the direction that davidmoore and tiny-tim are recommending.

BTW, there are no such words in English as "intergral", "intergrate", or "intergration".