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# Analyzing problems involving definite integrals

AP.CALC: CHA‑4 (EU), CHA‑4.D (LO), CHA‑4.D.1 (EK), CHA‑4.D.2 (EK), CHA‑4.E (LO), CHA‑4.E.1 (EK)

## Problem

Consider the following problem:
The water level under a bridge is changing at a rate of r, left parenthesis, t, right parenthesis, equals, 40, sine, left parenthesis, start fraction, pi, t, divided by, 6, end fraction, right parenthesis centimeters per hour (where t is the time in hours). At time t, equals, 3, the water level is 91 centimeters. By how much does the water level change during the 4, start superscript, start text, t, h, end text, end superscript hour?
Which expression can we use to solve the problem?