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fix: add <cstdint> to math/**

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realstealthninja
2024-08-31 11:29:17 +05:30
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math/integral_approximation.cpp
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@@ -1,18 +1,29 @@
/**
* @file
* @brief Compute integral approximation of the function using [Riemann sum](https://en.wikipedia.org/wiki/Riemann_sum)
* @details In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth-century German mathematician Bernhard Riemann.
* One very common application is approximating the area of functions or lines on a graph and the length of curves and other approximations.
* The sum is calculated by partitioning the region into shapes (rectangles, trapezoids, parabolas, or cubics) that form a region similar to the region being measured, then calculating the area for each of these shapes, and finally adding all of these small areas together.
* This approach can be used to find a numerical approximation for a definite integral even if the fundamental theorem of calculus does not make it easy to find a closed-form solution.
* Because the region filled by the small shapes is usually not the same shape as the region being measured, the Riemann sum will differ from the area being measured.
* This error can be reduced by dividing up the region more finely, using smaller and smaller shapes. As the shapes get smaller and smaller, the sum approaches the Riemann integral.
* \author [Benjamin Walton](https://github.com/bwalton24)
* \author [Shiqi Sheng](https://github.com/shiqisheng00)
* @brief Compute integral approximation of the function using [Riemann
* sum](https://en.wikipedia.org/wiki/Riemann_sum)
* @details In mathematics, a Riemann sum is a certain kind of approximation of
* an integral by a finite sum. It is named after nineteenth-century German
* mathematician Bernhard Riemann. One very common application is approximating
* the area of functions or lines on a graph and the length of curves and other
* approximations. The sum is calculated by partitioning the region into shapes
* (rectangles, trapezoids, parabolas, or cubics) that form a region similar to
* the region being measured, then calculating the area for each of these
* shapes, and finally adding all of these small areas together. This approach
* can be used to find a numerical approximation for a definite integral even if
* the fundamental theorem of calculus does not make it easy to find a
* closed-form solution. Because the region filled by the small shapes is
* usually not the same shape as the region being measured, the Riemann sum will
* differ from the area being measured. This error can be reduced by dividing up
* the region more finely, using smaller and smaller shapes. As the shapes get
* smaller and smaller, the sum approaches the Riemann integral. \author
* [Benjamin Walton](https://github.com/bwalton24) \author [Shiqi
* Sheng](https://github.com/shiqisheng00)
*/
#include <cassert> /// for assert
#include <cmath> /// for mathematical functions
#include <functional> /// for passing in functions
#include <cassert> /// for assert
#include <cmath> /// for mathematical functions
#include <cstdint> /// for integral typedefs
#include <functional> /// for passing in functions
#include <iostream> /// for IO operations
/**