Applications of integration include calculating moments and centers of mass from "summary" of Skills in Mathematics - Integral Calculus for JEE Main and Advanced by Amit M Agarwal
One important application of integration is in the calculation of moments and centers of mass. Moments refer to the measure of the distribution of a given quantity about a specific axis or point. In physics and engineering, moments are crucial for understanding the balance and stability of objects. By using integration, we can determine the moment of a region with respect to a particular axis or point.
Centers of mass, on the other hand, are points in a system where the weighted relative position balances the distribution of mass. Calculating the center of mass involves finding the average position of all the points in a system, taking into account their mass distribution. Integration plays a key role in determining the center of mass for various geometric shapes and objects.
To calculate moments and c...
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