Question

Question #91038

Answer 1

Since `1/x` is decreasing, `R_n` gives you the lower sum, and `L_n` gives you the upper sum.

Explanation:

Let us split the interval `[1,3]` into 6 subintervals with endpoints:

`{1,4/3,5/3,2,7/3,8/3,3}`

and `Delta x=(b-a)/n=(3-1)/6=1/3`

Upper Sum: `L_6=(1/1+1/(4/3)+1/(5/3)+1/(2)+1/(7/3)+1/(8/3))cdot1/3`

Lower Sum: `R_6=(1/(4/3)+1/(5/3)+1/(2)+1/(7/3)+1/(8/3)+1/3)cdot1/3`

I hope that this was clear.