# Fundamental Theorem of Calc.!

• Apr 16th 2008, 11:28 AM
mathlete
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.

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

f(t) = 0.5t+4
• Apr 16th 2008, 12:04 PM
TheEmptySet
Quote:

Originally Posted by mathlete
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.

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