We summarize these findings in the following theorem. How are both of the above concepts and their corresponding use of definite integrals similar to problems we have encountered in the past involving formulas such as distance equals rate times time and mass equals density times volume?įigure 6.\] What is the total force exerted by water against a dam? How do we measure the work accomplished by a varying force that moves an object a certain distance? Common weight densities: Water 62.4 pounds per cubic footSeawater 64.0 pounds per cubic foot Pascal's principle: The pressure exerted by a fluid at a depth 2istransmitted equally in all directions. Section 6.5 Physics Applications: Work, Force, and Pressure Motivating Questions Pressure T A2 where Ais the weight-density of the liquid per unit of volume. Population Growth and the Logistic Equation To find the fluid force or pressure on a vertical surface we must use calculus.Qualitative Behavior of Solutions to DEs.An Introduction to Differential Equations.Physics Applications: Work, Force, and Pressure.Area and Arc Length in Polar Coordinates.Using Definite Integrals to Find Volume by Rotation and Arc Length.Using Definite Integrals to Find Area and Volume.Using Technology and Tables to Evaluate Integrals.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.Interpreting, Estimating, and Using the Derivative.
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