Let $f(x)=4x9,x_1=0,x_2=1,x_3=2,x_4=3,$ and $x=1.$

$($a$)$ Find ${\displaystyle \underset{i=1}{\overset{4}{}}}f(x_i)x.$

$($b$)$ The sum in part $($a$)$ approximates a definite integral using rectangles. The height of each rectangle is given by the value of the function at the left endpoint. Write the definite integral that the sum approximates.

$($a$){\displaystyle \underset{i=1}{\overset{4}{}}}f(x_i)x=$

$($Simplify your answer.$)$

$N$ an example