The areaA of the regionS that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles:

(a) Use this definition to find an expression for the area under the curvey=x^{3}from 0 to 1 as a limit

A= lim n-->infinity ( f(x1)1/n +f(x2)1/n + ...+f(xn)1/n )

x1= x1+deltax = 1*deltax

x2= 2deltax

x3= 3deltax

xi=ideltax= i(1/n)

My answer =

(b) Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a).

I am not sure at all how to solve this part.

Any help greatly appreciated!!