Quick integral

  • #1

Homework Statement



[itex]\int cos^{2}(bx)dx[/itex]

Homework Equations





The Attempt at a Solution



This integral popped up in my quantum mechanics class yesterday and I solved it through double substitution to get,
[itex]\frac{x}{2} + sin(bx) * \frac{1}{4b}[/itex].

My question is, someone in my class said there was an easier way to solve this that only took 2-3 lines. Does anyone here have any ideas on what that may be?
 

Answers and Replies

  • #2
DryRun
Gold Member
838
4
Use double angle formula to convert the integrand.
[tex]\cos 2(bx) = 2\cos^2 (bx) -1[/tex]
[tex]\int cos^{2}(bx)dx=\frac{1}{2} \int (cos 2(bx)+1)dx[/tex]
 
  • #3


Use double angle formula to convert the integrand.
[tex]\cos 2(bx) = 2\cos^2 (bx) -1[/tex]
[tex]\int cos^{2}(bx)dx=\frac{1}{2} \int (cos 2(bx)+1)dx[/tex]
Wow that makes it easier...haha always forget my trig identities. Cheers for the quick response.
 

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