How do I integrate cos^2(x)?

  • Google+ icon
  • LinkedIn icon

The key to solving any integral of this form is to use the cosine rule:

cos(2x) = cos2(x) - sin2(x) = 2cos2(x) - 1 = 1 - 2sin2(x)

All of these forms are really helpful when solving problems such as this, and it's great if you can remmeber them, though if you get stuck in an exam, they can all be derived from the addition formulae that are probably on your fomula sheet!

So, using the above idenities, we know that:

2cos2(x) - 1 = cos(2x)

2cos2(x) = cos(2x) + 1

cos2(x) = (cos(2x) + 1)/2

So instead, we perform the integral of (cos(2x) + 1)/2, which we already know how to do.

=> (sin(2x))/4 + x/2

Daniel F. A Level Maths tutor, A Level Further Mathematics  tutor, GC...

About the author

is an online A Level Maths tutor with MyTutor studying at Durham University

Still stuck? Get one-to-one help from a personally interviewed subject specialist.

95% of our customers rate us

Browse tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss