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December 1st, 2008, 01:02 AM   #1
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How would you solve this integral?

the integral of sin^2(u)cos(u) du (from 0 to 2pi)
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December 1st, 2008, 01:03 AM   #2
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Re: How would you solve this integral?

please help. i'm so confused. : (
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December 1st, 2008, 01:35 AM   #3
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Re: How would you solve this integral?

You have:



Try calculating this first:



Take the substitution:





Now you have:



Now the rest is simple..
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December 1st, 2008, 08:47 AM   #4
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Re: How would you solve this integral?

I'd not advise mixing variables in the same integral at the same time, nor substitution unless absolutely necessary. What you might consider is that a number of integral problems arise as a consequence of being the inverse of some already studied differential problems:



at which time you might consider that the curve is above the x-axis from 0 to Pi, and below from Pi to 2Pi.
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