How do I integrate cos^2(x)?

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

DF
Answered by Daniel F. Maths tutor

37301 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Evaluate gf(-5) for the functions f(x)=3x+7, g(x)=3x^2+6x-9


Differentiate the function X^4 - (20/3)X^3 + 2X^2 + 7. Find the stationary points and classify.


For which values of k does the quadratic equation 2x^2+kx+3=0 only have one unique solution?


Find the integral of (cosx)*(sinx)^2 with respect to x


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences