Build approximations to the definite integral L x dx using several Riemann sums and compare with...
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Build approximations to the definite integral L √x dx using several Riemann sums and compare with the exact result. (a) Define the given function √. Graph of the function is shown automatically on the plot area. You can "swich off the graph using circular button on the left from the input line. Similar switching buttons are present for all graphs and plots you create in Geogebra. (b) You will use the command Rectangle Sum (√,1/2,2,n,1/2) to calculate and visualize the Riemann sum in the case when the interval [1/2, 2] is divided into n subintervals. The last argument 1/2 in the brackets instructs the command to use middle points of subintervals in calculations of values of the function. The command Rectangle Sum (..) produces both numerical value of the Riemann sum and a plot of the rectangles. You can "swich off" the plot using circular button on the left from the input line. (c) Use the command RectangleSum (√,1/2,2, n, 1/2) to obtain numerical values of the Riemann sums with 4, 16, and 32 subintervals. To facilitate comparison, present numerical values as decimals. "Swich off" the plot with n=16 for clarity of the figure. (d) Use the command Integral (√x,x,1/2,2) to calculate exact value of the def- inite integral. Present numerical value as a decimal. "Switch off the plot pro- duced by this command. (e) Adjust plot area so that the graph of the function and the Riemann sums with 4 and 32 subintervals are clearly visible. (f) Save a screenshot of your calculations in (a)-(e): Build approximations to the definite integral L √x dx using several Riemann sums and compare with the exact result. (a) Define the given function √. Graph of the function is shown automatically on the plot area. You can "swich off the graph using circular button on the left from the input line. Similar switching buttons are present for all graphs and plots you create in Geogebra. (b) You will use the command Rectangle Sum (√,1/2,2,n,1/2) to calculate and visualize the Riemann sum in the case when the interval [1/2, 2] is divided into n subintervals. The last argument 1/2 in the brackets instructs the command to use middle points of subintervals in calculations of values of the function. The command Rectangle Sum (..) produces both numerical value of the Riemann sum and a plot of the rectangles. You can "swich off" the plot using circular button on the left from the input line. (c) Use the command RectangleSum (√,1/2,2, n, 1/2) to obtain numerical values of the Riemann sums with 4, 16, and 32 subintervals. To facilitate comparison, present numerical values as decimals. "Swich off" the plot with n=16 for clarity of the figure. (d) Use the command Integral (√x,x,1/2,2) to calculate exact value of the def- inite integral. Present numerical value as a decimal. "Switch off the plot pro- duced by this command. (e) Adjust plot area so that the graph of the function and the Riemann sums with 4 and 32 subintervals are clearly visible. (f) Save a screenshot of your calculations in (a)-(e):
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To build approximations to the definite integral 122 7 da using several Riemann sums and compare with the exact result follow these steps Approximatin... View the full answer
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South-Western Federal Taxation 2020 Comprehensive
ISBN: 9780357109144
43rd Edition
Authors: David M. Maloney, William A. Raabe, James C. Young, Annette Nellen, William H. Hoffman
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