How Do You Evaluate the Integral of arcsec(x) from sqrt(2) to 2?

[frasifrasi]

For the integral from sqrt(2) to 2

of
1 over x*sqrt(t^(2) - 1) dx

I noticed that this was just the arcsece, so I got arcsec(x) for the answer, but how would I evaluated this at 2 and sqrt(2)?


What did i do wrong?


Thank you!

 

[Defennder]

Why are there 2 variables in your integral? Is t supposed to be there? Can it be treated as a constant for this question?

 

[rocomath]

more clarity and a little more work would be appreciated

 

[frasifrasi]

Ok, the integral is:

1 over x*sqrt(x^(2) - 1) dx


--> which I evaluated to be arcsec (x),but this doesn't make sense with the limits of integration...

 

[rock.freak667]

Well if you want to find arcsec(\sqrt{2}) you can always work it out like this:

Let \alpha=sec^{-1}(\sqrt{2})

so that sec\alpha=\sqrt{2}
and therefore cos\alpha=\frac{1}{\sqrt{2}} and then you find \alphaOR...somewhere in you attempt you would have used the substitution x=sec\theta so from there you could have gotten \theta=cos^{-1}(\frac{1}{x}) and use that instead of arcsec

 

[frasifrasi]

Oh my god!