trig integral, from pi/2 to 0, of sin^5(x)cos^8(x)dx

dmsjr12

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Sep 7, 2007
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Ok I came across several integrals like this one in my homework, and I am at a complete loss for how to do them. If anyone could explain what to do and why to do it, it would be a huge help as I will almost definitely need to know this stuff not only for my homework but for my first test. Thanks guys.

[def. integral from pi/2 to 0] sin^5(x)cos^8(x)dx

I remember my professor saying something about even and odd with these problems, but I really didn't understand most of what he was talking about. If anyone could please help I would be very grateful.[/tex][/list]
 
sin<sup>5</sup>x cos<sup>8</sup>x =

sinx sin<sup>2</sup>x sin<sup>2</sup>x cos<sup>8</sup>x =

sinx(1 - cos<sup>2</sup>x)(1 - cos<sup>2</sup>x)cos<sup>8</sup>x =

sinx(1 - 2cos<sup>2</sup>x + cos<sup>4</sup>x)cos<sup>8</sup>x =

cos<sup>8</sup>x sinx - 2cos<sup>10</sup>x sinx + cos<sup>12</sup>x sinx

now, integrate each term above using the substitution u = cosx.
 
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