Question

Riemann Sum. I'm finding the midpoints and using that to estimate the area under a curve. I can't remember the formula for this.

Answer 1

I know that
\[\Delta x=\frac{37-5}{4}=8\]
form my problem
so now what. Also I' working with a table.

Answer 2

x 5 9 13 17 21 25 29 33 37
f(x) 5 5.8 6.9 8.8 9.6 8 6.5 5.3 4.2

Answer 3

\[f(5)\Delta x + f(5.8)\Delta x+f(6.9)\Delta x+...+f(n)\Delta x\]
depending if it's a left hand sum or a right hand sum you would neglect the first or last term on the table.

Answer 4

its the middle so it neither left or right.

Answer 5

so could I do something like this then
\[\Delta x(f(x)+f(x2)+f(x3).....)\]

Answer 6

if it's middle you have to just do left and right then add them then divide by 2 i think.