What is the area of the region in the first quadrant bounded from above by the graph of the line y=1/2 and from below by y=sinx on the interval x=0 to x=pi/6

Answer 1

The area between two function f(x) and g(x) with g(x)<f(x) for the domain in consideration:

Area = int(from x₁ to x₂) (f/(x)-g(x))

In this case, f(x) = 1/2 and g(x) = sin(x) integrating from 0 to π/6 which is the point when g(x) = 1/2

A = Int(from 0 to π/6) (1/2-sinx)dx

which I leave to you.