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An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of 

r(t) = 70e−0.05t liters per minute. How much oil leaks out during the first hour?

 Nov 30, 2016
 #1
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How large is the the mess? indecision

 

60070e0.05t=70e0.05tdt|Calculate the indefinite integral =70e0.05tdt| (Move constant) af(x)dx=af(x)dx

=7020eudu|f(x(g))g(x)dx=f(u)du,u=g(x)du=0.05dtdt=(20)du=ddt(0.05t)

 

=70(20eudu)| Move constant =70(20eu)| usingeudu=eu=70(20e(0.05t)|for u=0.05t=1400et20

 

1400e3=69.70| for t=601400e0=1400| for t=01400(69.70)=1330.31330 liters leak in the first hour

 

I’m glad I don’t have to mop this up. smiley

 Nov 30, 2016

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