# Integral Calculus Drained Tank

by Kyle Anderson   Last Updated July 12, 2019 07:20 AM

Is my answer to the question below correct??

i) $$(\frac{dv}{dt}) = 2t - 20 \Rightarrow V = 2 (\frac {t^2}{1} = dt$$ $$V(t) = t^2 - 20t + c \Rightarrow V(5) = 0 \Rightarrow$$ $$25 - 100 + c = 0 \Rightarrow c = 100-25 = 75 \Rightarrow c = 75$$ $$t = 0 \Rightarrow V(t) = 75$$ $$t=1 \Rightarrow V(1) = t^2 - 20t + 75$$

ii) $$V(4) = 16 - 80 + 75 = 11 Kilolitres$$

Is this correct? If not can anyone help??

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The answer to your first question appears to be correct. However, I understand the second question differently. The fourth minute does only last from 3:00 minutes to 4:00 minutes. Compare to how the first minute lasts from 0:00 to 1:00. You calculated the volume of the drained oil from 0:00 to 4:00. The question to that answer would be "How much oil is drained in the first four minutes".

Now that you know how much oil has been drained in the first four minutes, simply substract the oil that has been drained in the first three minutes, i.e. $$\int \limits_3^4 \frac{dv}{dt}dt$$

infinitezero
July 12, 2019 06:36 AM

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