How do you integrate (sinx)^2?

(sinx)^2 (similarly to (cosx)^2) cannot be integrated in this form. There is a standard method to get past this though, which makes use of the cos double angle formula:cos(2x) = (cosx)^2 - (sinx)^2        = 1 - (sinx)^2 - (sinx)^2        = 1 - 2(sinx)^22(sinx)^2 = 1 - cos(2x) (sinx)^2 = 1/2 - (1/2)cos(2x)So the integral of '(sinx)^2' can instead be seen as the integral of '1/2 - (1/2)cos(2x)'.This is a much easier integral to work out, and using our knowledge of integrating (the integral of cos(2x) is (1/2)sin(2x)) the answer is:(1/2)x - (1/4)sin(2x) + cAs the integration here is indefinite (without limits) the constant of integration must be present (+c).This is a method which is very specific to sinx and cosx, specifically when they are put to even powers.

WW
Answered by Will W. Maths tutor

38200 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the volume of revolution when the curve defined by y=xe^(2x) is rotated 2*pi radians about the x-axis between x=0 and x=1


If (x+1) is a factor of 2x^3+21x^2+54x+35, fully factorise 2x^3+21x^2+54x+35


Prove that the indefinite integral of I = int(exp(x).cos(x))dx is (1/2)exp(x).sin(x) + (1/2)exp(x).cos(x) + C


Differentiate 4x^2 + 2ln3x + e^x


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