MYTUTOR SUBJECT ANSWERS

3388 views

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
:)

Ella N. GCSE Maths tutor, A Level Maths tutor, A Level Further Mathem...

2 years ago

Answered by Ella, an A Level Maths tutor with MyTutor


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

311 SUBJECT SPECIALISTS

£24 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

£30 /hr

Anuradha D.

Degree: Physics (Masters) - Durham University

Subjects offered:Maths, Physics+ 4 more

Maths
Physics
Music
Further Mathematics
Chemistry
-Personal Statements-

“Hello everyone! My name is Anuradha (you can call me Anu), and I am a Physics Undergrad at Durham. I have always had a “thing” for science and am so pleased to be studying it – and hope that I can give you all the support you need to ...”

£20 /hr

John W.

Degree: Mathematics (Masters) - St. Andrews University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I've done a broad range of maths learning and tutoring over the years, now continuing this on to university I'm sure I'll be able to help you out! ”

About the author

Ella N.

Currently unavailable: until 01/09/2016

Degree: Mathematics G103 (Masters) - Warwick University

Subjects offered:Maths, German+ 2 more

Maths
German
Further Mathematics
-Personal Statements-

“I was lucky enough to have amazing teachers for my GCSEs and A-levels, so I know how helpful it can be to have someone reliable to help you through these crucial periods. I hope that I can provide you with this support and that we can...”

You may also like...

Posts by Ella

How do I use two-way prepositions?

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

How to use the integrating factor?

Other A Level Maths questions

How do I know which method of diffirentiation to use?

How do I differentiate sin^2(x)?

The polynomial p(x) is given by p(x) = x^3 – 5x^2 – 8x + 48 (a) (i) Use the Factor Theorem to show that x + 3 is a factor of p(x). [2 marks] (ii) Express p(x) as a product of three linear factors. [3 marks]

When using the addition rule in probability, why must we subtract the "intersection" to find the "union" with the Addition Rule?

View A Level Maths 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

mtw:mercury1:status:ok