Water flows from the bottom of a storage tank at a rate of r (t) = 300 - 6t liters per minute, where 0 ≤ t ≤ 50. Find the amount of water that flows from the tank during the first 35 minutes.

r (t) models the water flow rate, so the total amount of water that has flowed out of the tank can be calculated by integrating r (t) with respect to time t on the interval t = [0, 35]min

∫r (t) dt, t = [0, 35]

= ∫ (300-6t) dt, t = [0, 35]

= 300t-3t², t = [0, 35]

= 300 (35) - 3 (35) ² - 300 (0) + 3 (0) ²

= 6825 liters