MYTUTOR SUBJECT ANSWERS

208 views

How do you integrate the function cos^2(x)

At first, you might think that it is possible to perform this integral simply by inspection, using the 'backwards chain rule'. This method would consist of adding one to the power, to get cos3(x), then dividing by the new power and the derivative of the function, giving you -(1/3sin(x))cos3(x). However, once you have performed an integration it is always wise to check your result by differentiating to see if you get your starting function back. In this case, it is clear that differentiating -(1/3sin(x))cos3(x) does not give cos2(x), because you have to use the quotient rule to differentiate cos3(x)/sin(x).

This means that a different approach is required to perform the integration, and that is to use the trig identity cos2x=1/2+(1/2)cos(2x) to change the integrand to something which can be integrated easily. It is then simple to integrate 1/2 +(1/2)cos(2x) using the familiar method, giving the correct answer of (1/2)x+(1/4)sin(2x)+c (not forgetting the constant of integration!).

Similarly, sin2(x) can be integrated quickly using the trig identity sin2(x)=1/2-(1/2)cos(2x), so these two identities are definitely worth memorizing!

Edward R. GCSE Maths tutor, A Level Maths tutor, Uni Admissions Test ...

9 months ago

Answered by Edward, an A Level Maths tutor with MyTutor

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

182 SUBJECT SPECIALISTS

£24 /hr

Sarah O.

Degree: PhD in Physics (Doctorate) - Cambridge University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Chemistry

“I'm a first year Physics PhD student at the University of Cambridge. I completed my MChem (Chemistry degree) at the University of Warwick, for which I achieved a 1st. I have experience tutoring A-Level students Chemistry and Maths one...”

MyTutor guarantee

£20 /hr

Ben A.

Degree: Medicine (Bachelors) - University College London University

Subjects offered: Maths, Physics+ 6 more

Maths
Physics
Chemistry
Biology
.UKCAT.
.BMAT (BioMedical Admissions)
-Personal Statements-
-Medical School Preparation-

“Hello,I am a first year medical student at University College London, When I was in sixth form, I helped tutor the younger years and I always enjoyed it, so I decided to keep it on in my university years.My subjects are the three m...”

£20 /hr

Anezka E.

Degree: Mathematics (Bachelors) - Kings, London University

Subjects offered: Maths

Maths

“About me: I'm hopefully about to start my second year at King's College London. I've thouroughly enjoyed studying maths for many years now and would love to help out a maths lover or hater and hopefully convert the latter into the for...”

MyTutor guarantee

About the author

Edward R.

Currently unavailable: for new students

Degree: Physics (Masters) - Oxford, St John's College University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
.PAT.

“About Me I am an enthusiastic and approachable physics student at Oxford University. For as long as I can remember I have taken an active interest inscience and maths, and I have always been keen to pass my enthusiasm onto others. I ...”

You may also like...

Posts by Edward

How do I solve the quadratic equation x^2+4x+3=0

How do you integrate the function cos^2(x)

Other A Level Maths questions

How do you resolve forces?

Differentiate the function f(x) = x*sin(x)

Why bother with learning calculus?

Core 3 - Modulus: Solve the equation |x-2|=|x+6|.

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok