A region whose area is given
The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles.
The width of the interval a, b is b-a, so the width of each n strip is
where x0=a and xn=b . The right end points of the subintervals are xi=a+i∆x.
It is given that
The general formula of area is
Comparing these equations to each other,
Therefore, a=1, so b=4 since
This means fxi=xi
That means the required region is
The region is fx=x, 1≤x≤4