Solution of IDZ Ryabushko 9.3 - Variant 26

Section: Chapter 9. Definite Integral
Topic: Applications of the Definite Integral: Physics and Mechanics
Description: Calculation of work required to pump liquid from reservoirs of various shapes (cylinder, cone, pyramid, etc.), force of liquid pressure on a vertically submerged plate, coordinates of the center of mass of a homogeneous plane curve and figure.

Tasks:
Includes 5 subtopics: work of pumping liquid, force of liquid pressure, coordinates of the center of mass of a curve, coordinates of the center of mass of a plane figure, application of the definite integral in physics
Solution methods: method of elementary layers; integration for calculating work; formula for force of pressure; formulas for the center of mass; calculation of static moments

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