Can someone PLEASE explain to me how the integral of 2cos^2(t)sin(t) dt =-(2/3)cos^3(t) ???

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25-03-2015
Mathematics

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Can someone PLEASE explain to me how the integral of 2cos^2(t)sin(t) dt =-(2/3)cos^3(t) ???

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Please help me solve this

Hippalectryon Hippalectryon · Answer 1 · 2015-03-25T22:35:48+01:00

Hippalectryon Hippalectryon

25-03-2015

Do the change of variable [tex]u=\cos(t)\rightarrow du=-\sin(t)dt[/tex]

Then [tex]\int\2cos^2(t)\sin(t)dt=-2\int u^2du=-\frac{u^3}3=-\frac{2}3\cos^3(t)[/tex]

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