Dead leaves fall to the ground in an area of forest at a rate of r(t) = 3te^-t ounds per year, where t is the number of years after a forest fire. Find the total weight of the leaves that have fallen in the forest during the first 10 years after the fire.
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integral from 0 to 10 of 3te^(-t)
= -3 e^(-t) (t+1) from t = 0 to t = 10
= -3 e^(-10) (11) + 3 = 2.9985
= -3 e^(-t) (t+1) from t = 0 to t = 10
= -3 e^(-10) (11) + 3 = 2.9985