How much oil V leaks out during the first hour?

An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) liters per minute. How much oil V leaks out during the first hour?


r(t) = 100 e^(-0.02 t)How much oil V leaks out during the first hour?
If you think about it, the amount of oil leaking out is equal to the rate that the oil leaks out multiplied by the time over which it leaked out.


Amount=rate*time


Since the rate is represented by a function and the time is represented by x, then the product of them would equal the area under the curve over a give time interval. Noting that one hour=60 minutes, the amount can be expressed as


integral (from 0 to 60) of 100e^(-0.02t) dt


=integral (from 0 to 60) of 5000*-0.02e^(-0.02t) dt


=(5000e^(-0.02t))[from 0 to 60]


=5000e^(-0.02*60)-5000e^(-0.02*0)


=5000e^(-1.2)-5000*1


=5000e^(-1.2)-5000


= some numberHow much oil V leaks out during the first hour?
JUST INTEGRATE R(T) BETWEEN 0 AND 60 MINUTES

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