Area under curves and definite integrals from "summary" of Differential Calculus by S Balachandra Rao
The concept of finding the area under curves using definite integrals is a fundamental topic in calculus. When we have a function that represents a curve on a graph, we can calculate the area under that curve by using definite integrals. Definite integrals are a way of finding the exact area under a curve between two specific points on the x-axis. By defining the limits of integration, we can determine the exact area enclosed by the curve and the x-axis within those limits. To find the area under a curve using definite integrals, we first need to set up the integral with the function that represents the curve. We then define the limits of integration, which are the x-values where we want to calculate the area between. The integral of the function over the specified interval gives us the area under the curve between those two points. This process allows us to find precise areas under curves, even for complex functions that cannot be easily calculated by other methods. Definite integrals provide a powerful tool for solving various problems involving area, such as finding the area of irregular shapes or the area between multiple curves. By using definite integrals, we can accurately determine the area under curves and solve a wide range of mathematical problems.- The concept of finding the area under curves using definite integrals is crucial in calculus and has many practical applications in mathematics and other fields. It allows us to calculate precise areas under curves and solve complex problems that require determining enclosed areas on a graph.
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