Question #91038

1 Answer
Wataru
Apr 19, 2017

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.

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