Find the area bounded by the curves y=sin(4x) and y=0 for x between x=0 and x=3pi/8.

Answer 1

Notice the period is 2π/4 or π/2 , (90°)
so your region is 1/2 a sine curve from 0 to π/4, plus a bit of the sine below the x-axis,
so take it in two parts,
from x = 0 to π/4 then the small bit below

don't forget to take
∫sin4x dx from 0 to π/4 + ∫-sin4x from π/4 to 3π/8