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Integration is a mathematical operation that involves finding the area under a curve. It is the inverse process of differentiation, which is finding the slope of a curve.
Integration is used in physics to calculate quantities such as velocity, displacement, and acceleration. In many cases, these quantities are represented by a curve, and integration allows us to find the exact values of these quantities at any given point.
Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both the magnitude and direction of the movement. Displacement, on the other hand, is a vector quantity that describes the change in position of an object from its initial position to its final position.
To find displacement from velocity, we use the fundamental theorem of calculus. This theorem states that the definite integral of a function is equal to the difference between the values of the function at the upper and lower limits of the integration.
Integration is used in physics to analyze motion, calculate work and energy, and determine the behavior of complex systems. It is also used in fields such as engineering, astronomy, and economics to model and solve various problems.