anonymous
  • anonymous
I have to integrate cos^2(x). Wolfram tells me that I will have to write cos^2(x) as (cos2(x)+1)/2 to proceed. Why is that? Isn't there a direct method of integrating trigonometric functions that have powers? If yes, why? :)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
potatoe potatoe
anonymous
  • anonymous
That didn't help.
amistre64
  • amistre64
its more effective when read in context :) its 2 different ways of getting to the same results

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amistre64
  • amistre64
i say potatoe, you say potatoe ....
amistre64
  • amistre64
the reduction formula is the "direct" method
amistre64
  • amistre64
lets see if i can recall it correctly:\[\int cos^n=\frac{1}{n}cos^{n-1}sin+\frac{n-1}{n}\int cos^{n-2}\]
anonymous
  • anonymous
Which method is more intuitive? I have opened an MIT lecture about power reduction on another tab, by the way.
amistre64
  • amistre64
cos^2 is small enough that rewriting it in its identity tends to be simpler than trying to recall the formula
amistre64
  • amistre64
the intergral of cos^n is by parts; whereas cos^2 is just an identity

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