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Math Topics

Applied Calculus

Integration: The Language of Accumulation

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1
Antidifferentiation and the Indefinite Integral

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2
Integration by Substitution

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3
The Definite Integral

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The Definite Integral and Area

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5
Improper Integrals

Suppose a pollutant is seeping into the ground near a dump site at the rate of \[f(t)=\frac{5\text{,}400}{(t+1.5)^3}\] liters per month, where \(t\) denotes the time from now in months. If the seepage of the pollutant continues indefinitely into the future, what is the total amount of pollutant that will seep into the ground?

Suppose the concentration of a particular drug that is administered orally is given by \(C_{po}(t)=100\left(e^{-0.5t}-e^{-0.8t}\right)\). The concentration of that drug when administered intravenously is given by \(C_{iv}150e^{-0.5t}\). This function considers both absorption and elimination of the drug over time. Determine the bioavailability, \(F\), of the drug.

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6
Integration by Parts

A manufacturer estimates that the relationship between the number of months, \(t\), from now and the number, \(N\), (in thousands) of units of a product she can produce per month is given by \[N(t)=14te^{-0.08t}\] Find the function that estimates the total production by the manufacturer if the total production initially is \(0\).