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Trig integral

  • #1
The question is to evaluate the integral in the attachment.

Using trig substition, I've reduced it to ∫ (tanz)^2 where z will be found using the triangle. I just need to integrate tangent squared which I can't seem to figure how to do. I tried using the trig identity (secx)^2 - 1 but I don't know what to do after.
 

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  • #2
arildno
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That is a good move.

Hint:
What do you get if you differentiate tan(z)?
 
  • #3
I get (sec(z))^2)
 
  • #4
arildno
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That is to integrate tan, I said differentiate it!
 
  • #5
Yes, sorry I realized I had made a mistake so when I differentiate tan, I get sec^2 ...
 
  • #6
arildno
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Indeed, so therefore you DO know an anti-derivative for sec^2, don't you?

Therefore, you should be able to find an anti-derivative for tan^2(z)=sec^2(z)-1
 
  • #7
So simple... thanks a lot
 

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