Integral (cos x)^2?

  • Thread starter teng125
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  • #1
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integral (cos x)^2??
the answer is 1/2x + 1/4 sin2x
pls help...thanx.....
 

Answers and Replies

  • #2
VietDao29
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teng125 said:
integral (cos x)^2??
the answer is 1/2x + 1/4 sin2x
pls help...thanx.....
To integrate something like sin2x dx, cos2x dx, we use Power-reduction formulas, ie:
[tex]\cos ^ 2 x = \frac{1 + \cos(2x)}{2} \quad \mbox{and} \quad \sin ^ 2 x = \frac{1 - \cos(2x)}{2}[/tex]
Can you go from here?
 
  • #3
LeonhardEuler
Gold Member
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You can do this using trig identities:
[tex]\cos{2\theta}=\cos^2{\theta}-\sin^2{\theta} = 2\cos^2{\theta}-1[/tex]
Now solve for [itex]\cos^2{\theta}[/itex]:
[tex]\cos^2{\theta}=\frac{1+\cos{2\theta}}{2}[/tex]
So
[tex]\int\cos^2{x}dx=\frac{1}{2}\int 1+\cos{2x}dx[/tex]
 

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