Area Problem - Riemann Sums - Left Endpoints - Right Endpoints | Calculus скачать в хорошем качестве

Area Problem - Riemann Sums - Left Endpoints - Right Endpoints | Calculus

In this calculus video I will show you how to estimate Area under graph of a function using Riemann sums. I will show you how to approximate the area under the curve using rectangles over a closed interval and I show you how to estimate the area of the region using left endpoints and right endpoints. 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 in numerical integration, i.e., approximating the area of functions or lines on a graph, where it is also known as the rectangle rule. It can also be applied for approximating the length of curves and other approximations. The sum is calculated by partitioning the region into shapes (rectangles, trapezoids, parabolas, or cubics) that together form a region that is 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 by the small shapes is usually not exactly 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.