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 $\alpha$OR...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!