evaluate:

after a trig sub I end up here:

I'm not sure where to go from here?

This is what I was thinking:

but not sure. Any help in finishing this is greatly appreciated!

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- Nov 6th 2007, 08:12 PMGot5onItImproper Intergrals...
evaluate:

after a trig sub I end up here:

I'm not sure where to go from here?

This is what I was thinking:

but not sure. Any help in finishing this is greatly appreciated! - Nov 6th 2007, 08:38 PMSoroban
Hello, Got5onIt!

Quote:

Evaluate: .

After a trig sub I end up here: . . . . . no

This is a standard form: .

So we have: .

- Nov 6th 2007, 08:41 PMJhevon
if you don't want to use the standard form for the answer, you could have used the trig substitution (after some algebraic manipulation), and you would arrive at the answer

(by the way, when you change the variable, the limits usually changes with it, in this case, when you went from t to , the limits would not be 2 to 4 anymore) - Nov 6th 2007, 09:07 PMGot5onIt
Thanks for the help!

I used the trig sub

and

and

Looks like I was all wrong or going the "unnecessary" route.:D - Nov 7th 2007, 04:08 AMKrizalid
When the discontinuity is visible (of course, if it's in the upper or lower integration limit, not on the interval , you can avoid the limit procedure, then evaluate. The rest is routine.

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Why do we have to apply trig. sub.? Before that, I suggest to set

Since you'll have an easy integral to evaluate, and the conclusion follows.