How to integrate cos^2(x) ? ("cos squared x")

We can't integrate cos^2(x) as it is, so we want to change it into another form. We can easily do this using trig identities.

1) Recall the double angle formula:

cos(2x) = cos^2(x) - sin^2(x).

2) We also know the trig identity sin^2(x) + cos^2(x) = 1, so combining these we get the equation cos(2x) = 2cos^2(x) -1.

3) Now, we can rearrange this to give: cos^2(x) = (1+cos(2x))/2.

4) So, we have an equation which gives cos^2(x) in a nicer form, which we can easily integrate using the reverse chain rule.

5) This eventually gives us an answer of:

x/2 + sin(2x)/4 +c

Answered by Ella N. Maths tutor

575720 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate 1/((1-x^2)^(1/2)) by substitution


Solve the equation 3sin^2(x) + sin(x) + 8 = 9cos^2(x), -180<X<180. Then find smallest positive solution of 3sin^2(2O-30) + sin(2O-30) + 8 = 9cos^2(2O-30).


Why do you differentiate in optimisation questions?


Find the first 3 terms and the sum to infinity of a geometric series with first term, 10 and common ratio 0.2


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy