Mathematics

Problem

Let

f(x)=x^{2}e^{-x}

on the interval

[0,3]

. (a) For

n

equal subintervals on

[0,3]

, write an expression in summation notation that represents the approximation of

\displaystyle\int_{0}^{3} f(x)\,dx

obtained by using the left endpoints of the subintervals. (b) Simplify the expression from part (a) so that it is of the form

\displaystyle \frac{3}{n}\sum_{k=0}^{n-1} g(k)

, where

g

is an explicitly defined function of

k

. (c) Compute the approximation in part (a) when

n=6

, giving your answer to four decimal places. a. (a) b. (b) c. (c)