# Math Help - upper and lower sums for intergral

1. ## upper and lower sums for intergral

write but do not evaluate expressions for the upper and lower sums for the intergral of 10^x dx [0,1]

i found delta x to be 1/n
found the ith sub interval to be [(i-1)/n, i/n] but got stuck when i had to find Un ( upper sum)= Mi (delta x), Mi being the max
did the same for the lower sum and go to the same point as above with the minimum value

also find an expression for Un-Ln and calculate lim(Un-Ln) as n approaches infinity, does it equal 0?
thanks

2. The function $10^x$ is an increasing function.
Therefore, the upper sum is the right-hand sum, while the lower sum is the left-hand sum.