What is the integral of the function y=cos^2x-sin^2x?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have to find the integral of y = (cos x)^2 - (sin x)^2.

We know that cos 2x = (cos x)^2 - (sin x)^2

=> y = cos 2x

Int[ cos 2x dx]

let 2x = y, dy/2 = dx

=> Int[(1/2)cos y dy]

=> (1/2) sin y + C

substitute y = 2x

=> (1/2)*sin 2x + C

The required integral is (1/2)*sin 2x + C

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team