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Trustted
 2 years ago
integrate sin^3X
Trustted
 2 years ago
integrate sin^3X

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Jonask
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sin^3x=\sin x \sin^2x\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1i think the gimmick is to rewrite this as \[\sin^2(x)\sin(x)=(1\cos^2(x))\sin(x)\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1then \[\sin(x)\sin(x)\cos^2(x)\] first integral is easy, second is a u  sub

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1or you can look at the "reduction" formula for sine on the inside cover of the back off your text and use \(n=3\)

Trustted
 2 years ago
Best ResponseYou've already chosen the best response.0HMMMM.. Tnx guys.. can u give me a site for online lessons

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[\sin^3x=\sin x \sin^2x\\\qquad=\sin x\frac{1\cos(2x)}2\\\qquad=\tfrac12\big(\sin x\sin x\cos(2x)\big)\\\qquad=\tfrac12\Big(\sin x\frac{\sin(3x)+\sin(x)}{2}\Big)\\\qquad=\frac {\sin x}2\frac{\sin(3x)}{4}+\frac{\sin(x)}{4}\]
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