The amount of water that has entered the pool over these five minutes is 42.5 gallons.
Given the rate at which water enter the pool W(t). To calculate the amount of water that has entered the pool over these five minutes, we integrate W(t) over the interval t = 0 to t = 5.
[tex]Amount\ of \ water=\int\limits^0_5 {W(t)} \, dt \\\\\\Amount\ of \ water=\int\limits^0_5 {(1+3t)} \, dt \\\\\\Amount\ of \ water=[t+1.5t^2]_0^5\\\\\\Amount\ of \ water=42.5\ gallons[/tex]
The amount of water that has entered the pool over these five minutes is 42.5 gallons.
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