Determine the antiderivative of y=sin x*cos^n x?

Expert Answers

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

We have to find the anti derivative of y = sin x*(cos x)^n

let cos x = y

=> dy/dx = -sin x

=> (-1)*dy = sin x dx

Int [ sin x*(cos x)^n dx]

=> Int [ (-1)* y^n]

=> (-1)* y^(n+1) / (n + 1)

substitute y = cos x

=> [-1/(n+1)]*(cos x)^(n+1)

The required anti derivative is [-1/(n+1)]*(cos x)^(n+1)

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