MYTUTOR SUBJECT ANSWERS

618 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 ...

1 year ago

Answered by Edward, an A Level Maths tutor with MyTutor


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

361 SUBJECT SPECIALISTS

PremiumTimothy N. A Level Design & Technology tutor, GCSE Design & Technolog...
£36 /hr

Timothy N.

Degree: Architecture and Environmental Engineering (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Design & Technology
-Personal Statements-

“Hi there, I have a passion for helping students achieve, and believe that with my 200+ hours of experience, we will be able to surpass the grades you want!”

£30 /hr

Joe C.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Hi, I'm Joe, an experienced tutor and a University of Bristol graduate with a first class Degree in Mathematics.”

£20 /hr

Jamie M.

Degree: Physics with Theoretical Physics (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
Further Mathematics
.STEP.
-Personal Statements-

“In my own A-Levels I developed skills that allowed me to achieve 4A*s and I want to share these techniques with any students willing to learn.”

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 ...”

MyTutor guarantee

|  7 completed tutorials

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

Sketch the graph of x^2+y^2-6x-4y=23

The quadratic equation 2x^2+ 6x+7 has roots a and b. Write down the value of a+b and the value of ab.

When integrating, why do we add a constant to the resulting equation?

What is Differentiation?

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