Question

liquid leaked from a damaged tank at a rate of ( r(t) ) liters per hour. the rate decreased as time passed and values of the rate at five - hour time intervals are shown in the table.

( t ) (hr)	( r(t) ) (l/hr)
5	8.2
10	7.7
15	7.1
20	6.7
25	4.9

find estimates for the total amount of liquid that leaked out using a left riemann sum and a right riemann sum for the 5 subintervals given.
left riemann sum: (\boxed{}) liters
right riemann sum: (\boxed{}) liters
note: enter answers as decimal values (accurate to 4 decimal places).
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Explanation:

Step1: Identify interval width

$\Delta t = 5 - 0 = 5$

Step2: Left Riemann sum calculation

Sum left endpoints × $\Delta t$:
$5 \times (8.8 + 8.2 + 7.7 + 7.1 + 6.7)$
$= 5 \times 38.5 = 192.5$

Step3: Right Riemann sum calculation

Sum right endpoints × $\Delta t$:
$5 \times (8.2 + 7.7 + 7.1 + 6.7 + 6.2)$
$= 5 \times 35.9 = 179.5$

Answer:

Left Riemann sum = 192.5000 liters
Right Riemann sum = 179.5000 liters