Use Riemann Sums to estimate the following solution using both left and right su

Question

Use Riemann Sums to estimate the following solution using both left and right sums for the given values for n.
oil is leaking out of a tanker damaged at sea. the damage to the tanker is worsening as evidenced by the increasing leakage each hour, recorded in the following table.
Time (hours) 0 1 2 3 4 5 6 7 8
Leakage (gal/ hr) 50 70 97 136 190 265 369 516 720
a.) give an upper and lower estimate of the total quantity of oil that has escaped after 5 hours.

b.) repeat part (a) for the quantity of oil that has escaped after 8 hours.


Please Show your work. thank you.

Explanation / Answer

the width of each is 1 so just add up the values of the leakage.
(a)for left add the first 5: 50 70 97 136 190=543
for right add the five starting with the second value: 70 97 136 190 265 =758
(b) for left use first eight: 50 70 97 136 190 265 369 516 =1693
for right use last eight: 70 97 136 190 265 369 516 720=2363

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