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February 16th, 2008, 01:55 PM   #1
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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.
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February 16th, 2008, 04:04 PM   #2
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You're right: arcsin((x − 8)/2) + C. Differentiate that to see why.
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February 16th, 2008, 06:53 PM   #3
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Ahhh, but what is the first step I should do to integrate?
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February 16th, 2008, 07:54 PM   #4
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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.
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February 16th, 2008, 08:28 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 -(x-16x+60). Now, complete the square like skipjack suggested, which is -(x-8) + 2.

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

Hence solved.
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February 17th, 2008, 07:30 AM   #6
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Ooh that is really simple, I forgot about completing the square. Thanks
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