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Integration and Its Applications · Paper 2 — Free Maths AI SL Practice Questions

1MasterySAQ-SIndefinite integrals and their properties6 marksPaper 2~9 min
A company models the rate of change of profit, in thousands of dollars per year, for a new product using the function P′(t)=12t e−0.2tP'(t) = 12t\,e^{-0.2t}, where tt is the time in years since the product was launched.
(a)
Find ∫12t e−0.2t dt\displaystyle\int 12t\,e^{-0.2t}\,dt. [3 marks]
(b)
Hence determine the total profit generated during the first 5 years, given that the profit at t=0t = 0 was zero. Give your answer to the nearest thousand dollars. [3 marks]
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