Integration method

[KindofSlow]

I need to integrate ∫ ((16 - x^2 - y^2)^(1/2)) dy I cannot figure out how to start, specifically, which method to use.If someone wouldn't mind giving me a method of integration hint, I would appreciate it. Thank you

 

[daon2]

I need to integrate ∫ ((16 - x^2 - y^2)^(1/2)) dy I cannot figure out how to start, specifically, which method to use.If someone wouldn't mind giving me a method of integration hint, I would appreciate it. Thank you

If it is not a double integral, it will be a bit ugly. How I would go about it:

\(\displaystyle \sqrt{16 - x^2 - y^2} = \sqrt{\left(\sqrt{16-x^2}\right)^2 - y^2}\)

Now let \(\displaystyle a=\sqrt{16-x^2}\)

Your integral is of the form

\(\displaystyle \displaystyle \int \sqrt{a^2-y^2} dy\)

Use the trig-sub \(\displaystyle y=a\sin\theta\)

 

[KindofSlow]

That worked! Took me a while but it worked perfectly. Thank you very much.