Hi, I would like to know the answer for y=cos^2x, 0< x <2π

Question

we are working with the area of a curve on integrate.

Answer 1

Area under curve is

      2π

A =   ∫    cos^2x  dx

       0

Recall the formulae cos^2x=(1+cos2x)/2

    2π

A =   ∫   (1+cos2x)/2  dx

       0

                 2π

     = (1/2)  ∫   (1+cos2x)  dx

                  0

                                        2π

    =(1/2)  (x+((sin2x)/2)

                                       0

    =(1/2)  (2π+0)

   =π square units