Unit 8: Applications of Integration

#131 Patrick is drinking water throughout the day and the rate at which he drinks water is given by the differentiable function W, where W(t) is measured in cups per day and t is measured in days. Which of the following expressions gives Patrick’s average amount of water, in cups per day, he drank from t = 0 to t = 4 days?

#134 A particle moves along a straight line with time t ≥ 0 and the velocity of the particle is given by the differentiable function, v(t). If v(a) = v(b) = v(c) = 0 and v(t) > 0 on a < t < b and v(t) < 0 on b < t < c, then which of the following expressions does not represent the total distance traveled by the particle on [a,c]?

#135 A particle moves along a straight line with time t ≥ 0 and the velocity of the particle is given by the differentiable function v(t) = cos(t). What is the total distance traveled by the particle from t = 0 to t = 2π?

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#136 A particle moves along a straight line with time t ≥ 0 and the acceleration of the particle is given by the differentiable function a(t) = 3t. What is the average acceleration of the particle from t = 0 to t = 4?

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#137 A person runs in a straight line across a field. The velocity of the person, v(t) is a differentiable function and selected values of v(t) are given above on the interval 0 ≤ t ≤ 10. Using a left Riemann sum with 4 subintervals are indicated by the table, what is the approximation of the average velocity of the person from t = 0 to t = 10?

• 2.2

• 2.7

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#138 Let R(t) be a differentiable function and represent the rate at which tea, measured in gallons per hour, is poured into a beverage machine after t hours for t ≥ 0. At t = 0 hours, there are 10 gallons of tea in the beverage machine. Which expression gives the total amount of tea in the beverage machine at t = 6 hours?

#139 Let D(t) be a differentiable function and represent the rate at which food is dispensed into a bowl for a cat measured in pounds per minute, after t minutes for t ≥ 0. Let E(t) be a differentiable function and represent the rate at which the cat eats food from the bowl, measured in pounds per minute, after t minutes for t ≥ 0. Which expression represents the change in the amount of food in the bowl, in pounds, from t = 1 to t = 6 minutes?

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