## QRAwarrior 3 years ago Suppose you have, in the denominator of your integral, the expression of the form x^2 - a^2. You want to use trigonometric substitution with this. How would the resulting triangle look like? ATTEMPT:

1. QRAwarrior

|dw:1337434470844:dw|

2. asnaseer

I'm sure I follow you, but some of the rules for trig substitution in integrals are described here: http://en.wikipedia.org/wiki/Trigonometric_substitution maybe that will help you.

3. asnaseer

*I'm NOT sure...

4. QRAwarrior

Got any ideas @shivam_bhalla?

5. shivam_bhalla

Your trigonometric substitution for such a case will be $x= asec (\theta)$ So $\sec(\theta)=x/a$ |dw:1337436343334:dw|

6. QRAwarrior

Yes!

7. shivam_bhalla

yes @QRAwarrior , you have done it correctly :)

8. QRAwarrior

Because I thought that there would be a side with "x^2 - a^2"

9. QRAwarrior

Anyways, thanks a lot.

10. shivam_bhalla

yw :)

11. apoorvk

okay, think about this --> if I have something like $\frac{1}{x^2 - a^2}$ I would be very happy, if I can reduce (x^2 - a^2) to a monomial. Right? Because that become very easy to integrate after I convert it into a form in the numerator. Now, if I remember the basics: $tan^2m +1 = sec^2m$ and $sin^2m + cos^2m = 1$ Now, I see, if I can get some think like a^2 *(sec^2(m) instead of the x^2, I can manage to get a a^2 tan^x in the denominator, and some ".....dm" in the numerator, which would be pretty easy to integrate then. So, I use the substitution: x=asecm and proceed. I get: dx= a secm tanm dm i plug this in the numerator in the place of dx. and then evaluate the integral pretty easily.

12. apoorvk

I just have to think of some ways to remove the radical sign if present, or make the denominator simpler.