Given $f ( x ) = e ^ { x } + x ; 0 \leq x \leq 2 , n = 6 ,$ set up a Riemann sum to approximate the area under the graph of f(x) on the given interval. Use the left endpoints. Is the following the correct sum?
$\frac { 1 } { 3 } \left[ 1 + \left( \mathrm { e } ^ { 1 / 3 } + \frac { 1 } { 3 } \right) + \left( \mathrm { e } ^ { 2 / 3 } + \frac { 2 } { 3 } \right) + ( \mathrm { e } + 1 ) + \left( \mathrm { e } ^ { 4 / 3 } + \frac { 4 } { 3 } \right) + \left( \mathrm { e } ^ { 5 / 3 } + \frac { 5 } { 3 } \right) \right]$

Question

Quizplus · Accepted Answer

The sum correctly represents a left Riemann sum for the function $f(x) = e^x + x$ over the interval $[0, 2]$ with $n = 6$ equal subdivisions, using the left endpoints of each subinterval to evaluate the function.

Given f(x)=ex+x;0≤x≤2,n=6,f ( x ) = e ^ { x } + x ; 0 \leq x \leq 2 , n = 6 ,f(x)=ex+x;0≤x≤2,n=6,

Given $f ( x ) = e ^ { x } + x ; 0 \leq x \leq 2 , n = 6 ,$