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Integrals of the form root(a^2 - x^2)need some help asap

conzy · 2009-05-18 11:30:06

I have an exam tomorrow and I have my integration down pretty well but questions like these: Give me a bit of trouble still, Could someone run through the technique quickly please? I think Im supposed to rewrite it as root( (3)^2 - (2x)^2) then let 2x = acosu? After that im pretty lost, Any help greatly appreciated, exam…

18-05-2009 11:30am

#1

conzy

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I have an exam tomorrow and I have my integration down pretty well but questions like these:

Give me a bit of trouble still, Could someone run through the technique quickly please?

I think Im supposed to rewrite it as root( (3)^2 - (2x)^2) then let 2x = acosu?

After that im pretty lost, Any help greatly appreciated, exam tomorrow

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#2 18-05-2009 2:14pm

LeixlipRed

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You're already half way there. So if you let 2x=3cosu the next step is to differentiate and change the integral into one in terms of u. Then you'll use the fact that 1-cos^2u=sin^2u. And then it's a matter of simplifying and you're away.

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