How do you find the integral of sin^2(x) dx?

Sin^2(x) cannot be integrated in its current form so you must use trigonometric identities to change sin^2(x) into something else.

Use the formula for cox(2x): cos(2x)=cos(x+x)=cos^2(x)-sin^2(x)

Now use that cos^2(x)=(1-sin^2(x))

So cos(2x)=1-2sin^2(x)

Rearrange the equation to find that sin^2(x)=1/2-1/2(cos(2x))

Now you can integrate to get that the integral of sin^2(x)=1/2x-1/4sin(2x)

Chloe W. GCSE Maths tutor, A Level Maths tutor, 11 Plus Maths tutor, ...

1 year ago

Answered by Chloe, an A Level Maths tutor with MyTutor

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


£20 /hr

Elliot D.

Degree: Mathematics (Bachelors) - St. Andrews University

Subjects offered:Maths, Physics


“Hi, I'm a 2nd year Computer Science student at St Andrews University. I mainly teach Maths at both GCSE and A-level.”

£22 /hr

Greg C.

Degree: Economics with Econometrics (Bachelors) - Exeter University

Subjects offered:Maths, Further Mathematics + 2 more

Further Mathematics
-Personal Statements-

“I consider myself a very extrinsic, hardworking person. I like to get involved in as much as I can and this is another opportunity to try something new! At the University of Exeter I’ve involved myself in a vast range of societies inc...”

MyTutor guarantee

£20 /hr

Jonathon B.

Degree: Theoretical Physics (Masters) - Queen's, Belfast University

Subjects offered:Maths, Physics


“I realised it is much more about problem solving! Using limited information to deduce the answers to real world problems with just pen, paper and mathematics”

MyTutor guarantee

About the author

£26 /hr

Chloe W.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics

Further Mathematics

“About Me:I'm Chloe and I'm a 2nd year maths student at Bristol university. I've always enjoyed working with numbers and I hope that I can encourage others to love working with them too!I've tutored both of my siblings through their...”

You may also like...

Other A Level Maths questions

What is the dot product of two vectors?

Find the set of values of x for which 3x^2+8x-3<0.

Express 4 sin(x) – 8 cos(x) in the form R sin(x-a), where R and a are constants, R >0 and 0< a< π/2

What is the difference between definite and indefinite integrals?

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