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

40391 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the general solution of the equation tan(2x + pi/2) = SQRT(3), giving your answer for x in terms of π in a simplified form.


Find the turning points of the curve y=2x^3 - 3x^2 - 14.


Solve dy/dx= (x√(x^2+3))/e^2y given that y=0 when x=1, giving your answer in the form y = f(x)


Given that f(x)= (4/x) - 3x + 2 find i) f'(x) and ii) f''(1/2)


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:

© 2026 by IXL Learning