this question is designed to be answered without a calculator. let r(t) represent the rate, in square feet…

this question is designed to be answered without a calculator. let r(t) represent the rate, in square feet per minute, at which a groundskeeper is mowing a lawn t minutes after 3 p.m. which expression represents the area, in square feet, of the lawn that is mowed between 3 p.m. and 5 p.m.? ∫₀² r(t)dt 1/2∫₀² r(t)dt ∫₀¹²⁰ r(t)dt 1/120∫₀¹²⁰ r(t)dt

this question is designed to be answered without a calculator. let r(t) represent the rate, in square feet per minute, at which a groundskeeper is mowing a lawn t minutes after 3 p.m. which expression represents the area, in square feet, of the lawn that is mowed between 3 p.m. and 5 p.m.? ∫₀² r(t)dt 1/2∫₀² r(t)dt ∫₀¹²⁰ r(t)dt 1/120∫₀¹²⁰ r(t)dt

Answer

Explanation:

Step1: Determine time - interval in minutes

The time interval from 3 p.m. to 5 p.m. is 2 hours. Since 1 hour = 60 minutes, 2 hours = 120 minutes.

Step2: Recall the definite - integral formula for total change

If (r(t)) is the rate of change of a quantity (in this case, the rate of mowing in square feet per minute), then the total change in the quantity over the interval ([a,b]) is given by (\int_{a}^{b}r(t)dt). Here, (a = 0) (corresponding to 3 p.m.) and (b=120) (corresponding to 5 p.m.), so the area of the lawn mowed is (\int_{0}^{120}r(t)dt).

Answer:

(\int_{0}^{120}r(t)dt)