# Computing upper and lower Riemann sums

Compute the lower and upper Riemann sums L(f, P$$_n$$) and U(f, P$$_n$$) for the following functions f(x) and the partition P$$_n$$ = {0, $$\frac{1}{n}$$, ..., $$\frac{n}{n}$$ = 1} of [0, 1]

I find the Riemann sums in general to just be very confusing

a) f(x) = x + 3

b) f(x) = 3 - x

c) f(x) = e$$^x$$

• what have you tried? Jun 14 '20 at 6:18

For a) we have $$L(f,P_n) = \sum_{i=0}^n \frac in \cdot3\cdot \frac in = n+\frac{1}{2 n}-\frac{3}{2}, \ \ U(f,P_n) = \sum_{i=0}^n \frac in \cdot 3\cdot\frac {i+1}n = n-1/n,$$ and the other functions can be handled in the same manner.