Find the area between x-axis and y=sin4x ( 0 - pi/2 )?

Question

Show culculation please .

Answer 1

I am assuming that (0-pi/2) means (0,pi/2)
y = sin4x goes through one complete cycle for x going from 0 to pi/2. The area above the axis equals the area below so the area between the x-axis and the sine wave is zero.

If area is considered to be positive, as when you are going to paint the area,

Area = 2 x integral of sin4x from 0 to pi/4 = 2 x -[ -1/4 - 1/4]= 1

Answer 2

The total area is 1 because

area between 0 - pi/4 = 1/2 above x axis
area between pi/4 - pi/2 =1/2 below x axis

Answer 3

Off hand, I'd expect an area of zero, since in a pi/2 interval, sin4x will have one full cycle.