How do I integrate sin^2(x)?

First, remember the compound angle formula for cosine:

cos(2x)=cos^2(x)-sin^2(x).  Now use the identity sin^2(x)+cos^2(x)=1 to give:

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

Rearranging this so we have sin^2(x)=1/2(1-cos(2x))

Replace this with the original integration and use the chain rule to get:

1/2(x-1/2sin(2x))+c

CD
Answered by Christopher D. Maths tutor

5459 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How would you use the following expression to approximate [(4-5x)/(1+2x)(2-x)] when x=5 (A2 pure)


Find the Binomial Expansion of (1-5x)^4.


A projectile is thrown from the ground at 30 degrees from the horizontal direction with an initial speed of 20m/s. What is the horizontal distance travelled before it hits the ground? Take the acceleration due to gravity as 9.8m/s^2


simplify a^m x a^n


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences