AP Calculus BC 8.3.1: Integral Meaning

Practice AP Calculus BC questions on interpreting a definite integral of a rate as the net change of the modeled quantity.

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The temperature of water in a tub at time t is modeled by a strictly increasing, twice-differentiable function W, where W(t) is measured in degrees Fahrenheit and t is measured in minutes. At time t=0, the temperature of the water is 55°F. The water is heated for 30 minutes, beginning at time t=0. Values of W(t) at selected times t for the first 20 minutes are given in the table above.

Use the data in the table to evaluate $\int_{0}^{20} W^{\prime}(t) d t$ . Using correct units, interpret the meaning of $\int_{0}^{20} W^{\prime}(t) d t$ in the context of this problem.

$\int_{0}^{20} W^{\prime}(t) d t=W(20)-W(0)=71.0-55.0=16$
The water has warmed by 16 °F over the interval from t=0 to t=20 minutes.

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CHA-4.D—Interpret the meaning of a definite integral in accumulation problems question 1