What is the area between the curve y=cos3x*sin-x, x axis and lines x=o and x=pi?

Expert Answers

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

We have to find the definite integral of y= - cos 3x * sin x, in the limit x = 0 to x = pi.

Int [ - cos 3x * sin x]

=> Int [ cos 3x * sin dx]

=> Int [ (4(cos x)^3 - 3 cos x) sin x dx]

let cos x = u

=> du = -sin x dx

=> Int [ (2u^3 - 3u) du]

=> 2 u^4 / 4 - 3u^2 / 2

substitute u = cos x

=> 2* (cos x)^4 / 4 - 3* (cos x)^2 / 2

At x = pi

=> 2* 1/ 4 - 3 / 2 + C

At x = 0

=> 2* 1/ 4 - 3 / 2 + C

Subtracting the two we have

2* 1/ 4 - 3 / 2 + C - ( 2* 1/ 4 - 3 / 2 + C)

=>0

Therefore the required value of the area is 0.

Approved by eNotes Editorial Team

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial