Integral of sin^2(x) with respect to x

It is impossible to dirctly integrate sin^2(x) so we must transform it into something that can be integrated. Trigonometry can be used to do this. Recall the identity cos(2x) = cos^2(x) - sin^2(x) and cos^(x) + sin^2(x) = 1. These 2 indentities can be combined through a little bit of algebra to give; sin^2(x) = 0.5 -  0.5cos(2x). Now this is an expression which can be directly integrated! 

The integral of 0.5 - 0.5cos(2x)  is simply 0.5x -0.25sin(2x) 

OF
Answered by Orlando F. Maths tutor

13471 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Intergrate ln(x) with resepct to x


Find ∫ x^2(ln(4x))dx


A curve C with an equation y = sin(x)/e^(2x) , 0<x<pi has a stationary point at P. Find the coordinates ofP?


Given that y = 16x + x^(-1), find the two values of x for which dy/dx = 0


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning