What is the integral of sin^2(x)?

From the double angle formula for cosine, we know that cos(2x)=cos2(x)-sin2(x). Also, we know that sin2(x)+cos2(x)=1. So by substituting the second formula into the first, we can say that cos(2x)=(1-sin2(x))-sin2(x)=1-2sin2(x)

By rearranging, this gives sin2(x)=1/2-1/2cos(2x). Now, the right hand side of this equation can be more easily integrated with regards to x.

The integral of cos(ax) is (1/a)sin(ax). So, the indefinite integral of the RHS (and hence sin2(x)) is (1/2)x-1/4sin(2x)+C for some arbitrary constant, C.

JB
Answered by Jonathan B. Maths tutor

5707 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The function f has domain (-∞, 0) and is defines as f(x) = (x^2 + 2)/(x^2 + 5) (here ^ is used to represent a power). Show that f'(x) < 0. What is the range of f?


Differentiate: (12x^3)+ 4x + 7


Integrate sec^2(x)tan(X)dx


Consider the curve y=x/(x+4)^0.5. (i) Show that the derivative of the curve is given by dy/dx= (x+8)/2(x+4)^3/2 and (ii) hence find the coordinates of the intersection between the left vertical asymptote and the line tangent to the curve at the origin.


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