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

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

Recall the double angle formula: cos(2x) = cos^2(x) - sin^2(x). 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.

Now we can rearrange this to give: cos^2(x) = (1+cos(2x))/2.
So we have an equation which gives cos^2(x) in a nicer form which we can easily integrate using the reverse chain rule.

This eventually gives us an answer of x/2 + sin(2x)/4 +c
:)

Answered by Ella N. Maths tutor

412286 Views

See similar Maths A Level tutors
Illustration of a video tutorial

Need help with Maths?

One to one online tuition can be a great way to brush up on your Maths knowledge.

Have a Free Meeting with one of our hand picked tutors from the UK’s top universities

Find a tutor

Related Maths A Level answers

All answers ▸

Where z is a complex number, what is the cartesian form of |Z-2+3i| = 1?


How would you integrate ln(x)


How do I simplify (1 / [1 + cos(x) ] ) + (1 / [1 - cos(x) ] )?


Solve the equation sec^2(A) = 3 - tan(A), for 0<= A <= 360 (degrees)


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 2013–2022

Terms & Conditions|Privacy Policy