2. Let f(x) = ksin(kx), where k is a positive constant. Find the area of the region bounded by one arch of the graph of f and the x-axis

Answer 1

let's look at the first arch starting at the origin.
the period of ksin(kx) is 2π/k
so the arch goes from 0 to π/k

Area = ∫(ksin(kx) dx from 0 to π/k
=[ - cos(kx) ] form 0 to π/k
= -cos(π) - (-cos0))
= -(-1) + 1
= 2