# Why is this happening (trig subs)

1. Dec 18, 2007

### frasifrasi

Dor the integral 1/x*sqrt(t^2 - 1)

After i do the substitutions, it comes out to be sec(x)tan(x)/sec(x)tan(x), so evertything cancels out and the integral evaluated is just x (or theta), but what do I sub theta for when evaluating the integral?

I know this is supposed to be arcsec, but I am not visualizing how I get to that point.

Thank you.

2. Dec 18, 2007

### rocomath

two variables ... which variable are you integrating with respects to?

3. Dec 18, 2007

### frasifrasi

theta...

I guess I have to change the limits of integration.

4. Dec 18, 2007

### rocomath

5. Dec 18, 2007

### frasifrasi

yes, letting x= sec$\theta$

If i let sqrt(2) = sec$\theta$ , I am looking for arcsec(sqrt(2)) , which is pi/ 4 since cos (pi/4) = 1/sqrt(2), so I would convert the limits. I gorgot that was required since we are mostly doing indefinite integrals.

6. Dec 18, 2007

### HallsofIvy

Staff Emeritus
No that wasn't the question- your original integral involves both x and t. Was that an typo? Did you mean dx/(x*sqrt(x^2-1)) or dt/(t*sqrt(t^2-1))?

7. Dec 18, 2007

was typo.