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ynot24one

Joined: Jul 15, 2006
Posts: 3
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Can you make sense of this simpification.

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I'm following my notes from class and can't figure out how this expression was simplified.

/ cos t (sin^4 t)dt = sin^5 t
C

thanks...pdt

[Jul 15, 2006 8:28:24 PM]

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pskinner

Joined: Apr 2, 2005
Posts: 797
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Re: Can you make sense of this simpification.

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Not exactly sure what to make of C in:

/ cos t (sin^4 t)dt = sin^5 t
C

But if the problem is to integrate cos(t)*(sin(t))^4 as an indefinite integral, you can use a u-substitution, where u=sin(t) and du=cos(t)dt, so you can now integrate u^4*du and get (u^5)/5 +C. After substituting back, this becomes ((sin(t))^5)/5+C, which is "similar" to your notes (but fills in the details).
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Principal Skinner

[Jul 16, 2006 8:52:57 AM]

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