The main task in each such problem is to determine the volume of a representative slice, followed by the force exerted on the slice, as well as the distance such a slice moves.
The preceding example demonstrates the standard approach to finding the work required to empty a tank filled with liquid. When evaluated using appropriate technology, the integral shows that the total work is \(W = 3463.2 \pi\) foot-pounds. Population Growth and the Logistic Equation.Qualitative behavior of solutions to DEs.An Introduction to Differential Equations.Physics Applications: Work, Force, and Pressure.Using Definite Integrals to Find Volume.Using Definite Integrals to Find Area and Length.Other Options for Finding Algebraic Antiderivatives.The Second Fundamental Theorem of Calculus.Constructing Accurate Graphs of Antiderivatives.Determining distance traveled from velocity.Using derivatives to describe families of functions.Using derivatives to identify extreme values.Derivatives of Functions Given Implicitly.Derivatives of other trigonometric functions.Limits, Continuity, and Differentiability.
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