- #1
phys-lexic
- 29
- 0
In doing math I try not to memorize shortcuts/simplifications, but instead understand what's happening. When studying integrals, my professor gave out a few "simplifications" for us to use on problems; most of which I have been able to figure out, except one. I just cannot seem to figure out the relationship given, please help clarify/explain. Thankyou.
[tex]\int(\sqrt{a^2-u^2})du[/tex] = [tex]\left(\frac{u}{2}\right)[/tex][tex]\times[/tex][tex]\left(\sqrt{a^2-u^2}\right)[/tex] + [tex]\left(\frac{a^2}{2}\right)[/tex][tex]\times[/tex][tex]\left(sin^{-1}\left(\frac{u}{a}\right)\right)[/tex] + C
I have tried:
- u substitution
- trig substitution
- IBP
*It could be my steps, maybe I'm just doing the intermediates wrong.
**it took a really long time to put that formula in
[tex]\int(\sqrt{a^2-u^2})du[/tex] = [tex]\left(\frac{u}{2}\right)[/tex][tex]\times[/tex][tex]\left(\sqrt{a^2-u^2}\right)[/tex] + [tex]\left(\frac{a^2}{2}\right)[/tex][tex]\times[/tex][tex]\left(sin^{-1}\left(\frac{u}{a}\right)\right)[/tex] + C
I have tried:
- u substitution
- trig substitution
- IBP
*It could be my steps, maybe I'm just doing the intermediates wrong.
**it took a really long time to put that formula in