My Math Forum Stuck on an Integration problem

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 February 16th, 2008, 02:55 PM #1 Newbie   Joined: Feb 2008 Posts: 13 Thanks: 0 Stuck on an Integration problem I am not sure how to do this problem, here it is. int 1/sqrt((x-6)(10-x)) I think the answer is something with arcsine but I am not sure how to get it.
 February 16th, 2008, 05:04 PM #2 Global Moderator   Joined: Dec 2006 Posts: 19,981 Thanks: 1853 You're right: arcsin((x âˆ’ 8)/2) + C. Differentiate that to see why.
 February 16th, 2008, 07:53 PM #3 Newbie   Joined: Feb 2008 Posts: 13 Thanks: 0 Ahhh, but what is the first step I should do to integrate?
 February 16th, 2008, 08:54 PM #4 Global Moderator   Joined: Dec 2006 Posts: 19,981 Thanks: 1853 The first step is called "completing the square", but you wouldn't be asking about that if, as I suggested, you'd verified the answer by differentiating it.
February 16th, 2008, 09:28 PM   #5
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Quote:
 Originally Posted by Gotovina7 Ahhh, but what is the first step I should do to integrate?
If you want to know if skipjack's answer is correct, take the derivative of arcsin((x ? 8)/2) + C. If you want to solve it on your own, first you expand (x-6)(10-x), which is -(x²-16x+60). Now, complete the square like skipjack suggested, which is -(x-8)² + 2².

?? 1/?((x-6)(10-x)) dx
= ? 1/?(2² - (x-8)²) dx
(? 1/?(a² - u²) du = arcsin(u/a) + C, in general)
= arcsin((x - 8)/2) + C

Hence solved.

 February 17th, 2008, 08:30 AM #6 Newbie   Joined: Feb 2008 Posts: 13 Thanks: 0 Ooh that is really simple, I forgot about completing the square. Thanks

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