the amount of gasoline stored at a fuel station is decreasing at a rate of r(t) liters per hour (where t is…

the amount of gasoline stored at a fuel station is decreasing at a rate of r(t) liters per hour (where t is the time in hours). what does ∫₂₀²¹ r(t) dt = -450 mean? choose 1 answer: a during the 21st hour, the amount of gasoline at the fuel station decreased by 450 liters. b during the first 21 hours, the amount of gasoline at the fuel station decreased by 450 liters. c during the first 20 hours, the amount of gasoline at the fuel station decreased by 450 liters. d during the 20th hour, the amount of gasoline at the fuel station decreased by 450 liters.

the amount of gasoline stored at a fuel station is decreasing at a rate of r(t) liters per hour (where t is the time in hours). what does ∫₂₀²¹ r(t) dt = -450 mean? choose 1 answer: a during the 21st hour, the amount of gasoline at the fuel station decreased by 450 liters. b during the first 21 hours, the amount of gasoline at the fuel station decreased by 450 liters. c during the first 20 hours, the amount of gasoline at the fuel station decreased by 450 liters. d during the 20th hour, the amount of gasoline at the fuel station decreased by 450 liters.

Answer

Explanation:

Step1: Recall integral meaning

The definite - integral $\int_{a}^{b}r(t)dt$ represents the net change of the amount of gasoline from time $t = a$ to time $t = b$, where $r(t)$ is the rate of change of the amount of gasoline.

Step2: Identify limits of integration

Here, $a = 20$ and $b = 21$, and $\int_{20}^{21}r(t)dt=-450$. The negative sign indicates a decrease.

Answer:

A. During the $21^{\text{st}}$ hour, the amount of gasoline at the fuel station decreased by 450 liters.