Why is this happening (trig subs)

[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.

 

[rocomath]

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

 

[frasifrasi]

theta...

I guess I have to change the limits of integration.

 

[rocomath]

once again, refer back to your old post

read what rock.freak commented to you

https://www.physicsforums.com/showpost.php?p=1543556&postcount=5

 

[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.

 

[HallsofIvy]

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.

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

theta...
I guess I have to change the limits of integration.

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))?

 

[frasifrasi]

was typo.