Let on the interval

MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

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

on the interval

[0,3]

. For

n

equal subintervals on

[0,3]

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

\displaystyle\int_0^3f(x)\,dx

obtained by using the left endpoints of the subintervals. Simplify the expression so that it is of the form

\displaystyle\frac3n\sum_{k=0}^{n-1}g(k)

, where

g

is an explicitly defined function of

k

. Compute the approximation when

n=6

, giving your answer to four decimal places. (1) (a) (2) (b) (3) (c)