Use this definition with the right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit.

Question

f(x)= 3+sin^2(x) 0<=x<=pi

Definition provided: The area of A of region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles.

Work done: a=0 b=pi
change of x= (pi-0)/n
(I don't know how to format the rest of my work properly on here, so I guess I'll just say that the answer I got within the summation was 3+sin^2(i*(pi/n)

I have no idea why I'm wrong, could I have some help?

Answer 1

consider the area as a set of rectangles of width π/n
The right endpoints are iπ/n for i=1..n
So the area is

n
∑ (3+sin^2(iπ/n))(π/n)
i=1

I guess you forgot to multiply by the width of the rectangles. You just added up the heights.