
Riemann sum Question
Consider the given function.
f(x) = 4  (1/4)x
Evaluate the Riemann sum for 2 ≤ x ≤ 4 , with six subintervals, taking the sample points to be left endpoints. (Give an exact answer.)
L6 =
How do I start this? and how do i know if its upper or lower bound?

So you are calculating $\displaystyle L_6$, meaning you have to divide the interval into six equal portions. And to find how long each of the subinterval is going to be, you will have to use this formula: $\displaystyle \frac {ba}{n} $
For $\displaystyle a \leq x \leq b $ dividing into n subintervals.
So, you should have $\displaystyle \frac {42}{6} = \frac {1}{3} $ as the length of your subs.
Now, you need to use the formula: $\displaystyle \frac {ba}{n} [ f(x_0)+f(x_1)+...+f(x_{n1}) ]$
Note that $\displaystyle x_0 = a =2$ and $\displaystyle x_n = b =4$, so $\displaystyle x_{n1} $ in this case is equal to $\displaystyle b  \frac {1}{3} = 4  \frac {1}{3} = \frac {11}{3}$, because we are using the left end points
So once you have plugged in all the value, you should have the following expression:
$\displaystyle \frac {1}{3} [ f(2)+f(2+ \frac {1}{3})+f(2+ \frac {2}{3}) + . . . + f( \frac {11}{3} ) ] $
Using $\displaystyle f(x)= 4  \frac {1}{4}x $, just plug in the values! Can you take it from here?
