Find the area

Question

Find the area of the region bounded by the graphs of y = 1 and y = cos2(x) from x = 0 to x = π.

Answer 1

As a problem solving strategy for this problem you might realize that the line 1-cos² exactly cuts the rectangle [0,pi]X[0,1] into areas that correspond. Because the minima in the function have the same shape as the maxima in the function you get pi/2. Think of areas as they "invert". It helps if you already have the function pre-graphed. No calculus necessary.

Answer 2

= definite integral of (1 - cos²x) dx  with upper limit b = pi, lower limit a = 0

 

Answer is pi/2

 

Note that I have assumed the 2nd function is the square of cos x.