Integration can be used to find the average value of a function over an interval from "summary" of Skills in Mathematics - Integral Calculus for JEE Main and Advanced by Amit M Agarwal
To find the average value of a function over an interval using integration, we need to consider a function f(x) defined on the closed interval [a, b]. The average value of this function over the interval [a, b] can be calculated by dividing the integral of the function over the interval by the length of the interval (b - a). Mathematically, the average value of the function f(x) over the interval [a, b] is given by: \[f_{avg} = \frac{1}{b - a} \int_{a}^{b} f(x) dx\] This formula essentially represents the total area under the graph of the function f(x) over the interval [a, b] divided by the length of the interval. By finding this average value, we can obtain a single representative value that captures the overall behavior of the function over the interval. The concep...
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