Left hand Riemann sum e^sin(x) left endpoints rectangle approximation of integral e^sin(x). скачать в хорошем качестве

Left hand Riemann sum e^sin(x) left endpoints rectangle approximation of integral e^sin(x).

Subscribe to Zak's Lab    / @zakslab   Questions or requests? Post your comments below, and I will respond within 24 hours. Left hand Riemann sum e^sin(x) left endpoints rectangle approximation of integral e^sin(x). To compute a left side Riemann sum, we break the interval into n subintervals so we can approximate the area by slicing into thin rectangles. Next, we approximate the area under the curve with rectangles where the height is measured at the left side of each rectangle. This is called a "left side rectangle approximation", "left side Riemann sum" or "left endpoints Riemann sum". We express the Riemann sum in summation notation. We work an example of a left endpoint Riemann sum. We are given the function f(x)=e^sin(x) on the interval [-1,1] and we set up a left sided Riemann approximation by computing delta x for the Riemann sum as the interval width divided by the number of rectangles. Next, we express x_i for the ith cutpoint for the subintervals. Finally, we express the Riemann sum in sigma notation. To get a decimal approximation for the Riemann sum, we use the computer algebra system wxMaxima to input the sum and obtain the area under e^sin(x) on [-1,1] to the thousandths place. We comment on the fact that this Riemann sum underestimates the definite integral because we have an increasing function. For a left sum increasing function, every rectangle has a small gap at the top, so each rectangle underestimates the area systematically. We compare our left area approximation computer algebra answer to the built in numerical integration algorithm quad-qag with favorable results.