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Integration of cos 3(cubed) x dx (1 Viewer)

Irskin

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Can anyone please help me out in re-arranging this question, using trig results/identities to make the integration simple??? Cheers
 

Trev

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int. cos<sup>3</sup>x dx
since cos<sup>2</sup>x=1-sin<sup>2</sup>x
Integral becomes:
int. cosx(sin<sup>2</sup>x-1) dx
You should be able to do the rest just by looking at it or using the substitution u=sinx.
 
P

pLuvia

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int[cos3x]dx
Let u=sinx du=cosxdx
int[cos2x]du
int[1-u2]du
=u-1/3u3+C
=sinx-1/3sin3x+C
 

shinji

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hmm. i thought we weren't expected to learn the integral of cos3x in 3unit maths..... besdides the onse where you have the 2 trig functions beside eachother.
i.e: sinx.cos2x ds
 

Mountain.Dew

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peoples, not to worry...in the HSC exams, they break the question into parts, e.g. get u to do a differential, maybe show that cos<sup>3</sup>x dx = cosxsin<sup>2</sup>x - cosx, THEN get u to do the intergation.

this makes the question easier to do, particularly since it is the 2U and 3U level.
 
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pLuvia

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That would take longer though. But if you're really desparate
 

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