Use the definition to find an expression for the area under the curve y = x3 from 0 to 1 as a limit. lim n→∞ n i = 1 r (b) the following formula for the sum of the cubes of the first n integers is proved in appendix e. use it to evaluate the limit in part (a). 13 + 23 + 33 + + n3 = n(n + 1) 2 2

The summand (R?) is missing, but we can always come up with another one.

Divide the interval [0, 1] into subintervals of equal length :

Let's consider a left-endpoint sum, so that we take values of where is given by the sequence

with . Then the definite integral is equal to the Riemann sum

i think this could be a possible answer (1 / 84) -1

good luck! : d