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Math Help - Fundamental Theorem of Calc.!

  1. #1
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    Fundamental Theorem of Calc.!

    Oil leaks out of a tanker at a rate of r = 0.5t + 4 gallons per minute, where t is in minutes.

    (a) Write a definite integral for the total gallons of oil that leak out of the tanker in the first two hours.
    Give your answer using the form

    so i found f(t) but how do i find A and B? any help...thanks

    f(t) = 0.5t+4
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    Quote Originally Posted by mathlete View Post
    Oil leaks out of a tanker at a rate of r = 0.5t + 4 gallons per minute, where t is in minutes.

    (a) Write a definite integral for the total gallons of oil that leak out of the tanker in the first two hours.
    Give your answer using the form

    so i found f(t) but how do i find A and B? any help...thanks

    f(t) = 0.5t+4
    your rate r is change in amount over the change in time so

    \frac{dA}{dt}=r=\frac{0.5t+4 \mbox{ Gal}}{min}

    so for the bounds on the integral we need to convert from hours into min

    2 hr =120 min. You could also change the rate into gal per hr and then just integrate from 0 2 instead of 0 to 120 min.
    your final answer should look like

    A=\int_{0}^{120}(0.5t+4)dt \mbox{ or } \int_{0}^{2}(30t+240)dt
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