integration and too many letters

[jessi1236w]

I am having trouble integrating the equation square root of (r squared minus x squared) on the bounds of negative r to negative r plus h. O and x is the only true variable, the others can be treated like numbers.

Basically, so far I've decided to use sin subsitution for x and that worked well until I have to either stick x back in or subsitute the bounds of subsitution. The second path seems much more logical. I don't really even know if a trig subsitution was the right choice. Ideas?[/code]

 

[galactus]

I assume you're referring to this: http://www.freemathhelp.com/forum/viewtopic.php?t=21302

Here it is, done by technology. (To heck with the thing otherwise.)

\(\displaystyle \L\\2L\int_{-r}^{-r+h}\sqrt{r^{2}-x^{2}}dx\)

=\(\displaystyle \L\\\frac{L{\pi}r^{2}}{2}-Lr^{2}sin^{-1}(\frac{r-h}{r})-Lr\sqrt{h(2r-h)}+Lh\sqrt{h(2r-h)}\)

 

[stapel]

...so far I've decided to use sin subsitution....

Actually, the tutors set it up for you using a sine substitution. Did you not notice that both tutors said that technology would be the way to go...?

In the future, please post follow-ups to threads within those originating threads. And always show what you're working with. Asking for "ideas" when all you've apparently asked is "I'm doing something with some letters" leaves the tutors with nothing to work with (until they find the other thread with the other tutors' work).

Thank you for your consideration.

Eliz.

 

[galactus]

If you insist on doing this thing the long way, instead of tech, look up the form in a table of integrals. We could derive it, but why?.

\(\displaystyle \L\\\int\sqrt{r^{2}-x^{2}}dx=\frac{x}{2}\sqrt{r^{2}-x^{2}}+\frac{r^{2}}{2}sin^{-1}(\frac{x}{r})+C\)

Use your limits of integration, -r and h-r, and see if you get the form I posted above.