AP Calculus AB Problems with Solutions (Part - 15)

Problem 1 :

As a pot of tea cools, the temperature of the tea is modeled by a differentiable function H for 0 ≤ t ≤ 25 where time t is measured in minutes and temperature H'(t) is measured in degrees Celsius per minute. Values of H'(t) at selected values of time t are shown in the table above.

(a) What is the average rate of temperature from 7 minutes to 18 minutes ? (Using right Riemann sum if necessary.)

(b) Indicate the unit and justify the (a) answer.

Solution :

Problem 2 :

Use the Trapezoid Riemann Sum Rule to approximate the area of the shaded region from t = 0 to t = 5 with 5 equal subintervals.

Solution :

Problem 3 :

Find the indefinite integral. (Use C for the constant of integration.)

Solution :

Problem 4 :

Find the indefinite integral. (Use C for the constant of integration.)

Solution :

Problem 5 :

Find the particular solution that satisfies the differential equation and the initial conditions.

f’’(x) = -2x + 3,   f’(2) = 6,  f(1) = 5

Solution :

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