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Use 73 rule with four segment, and i) Simpson's 3s rule ii) Simpson's to obtain the integration of: f(x) = 0.2+ 25.x- 200x² +675x - 900x* + 400x from a = 0 to b = 0.8.

Use 73 rule with four segment, and i) Simpson's 3s rule ii) Simpson's to obtain the integration of: f(x) = 0.2+ 25.x- 200x² +675x - 900x* + 400x from a = 0 to b = 0.8.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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а) Use i) Simpson's rule with four segment, and ii) Simpson's rule to obtain the integration of: f(x) = 0.2+ 25x – 200.x² + 675x – 900x* + 400.x from a = 0 to b 0.8. b) The trapezium rule, with 2 intervals of equal width, is to be used to find an approximate value for [e"dx. i) Explain with the aid of a sketch, why the approximation will be greater than the exact value of the integral. ii) Calculate the approximate value and the exact value, giving each answer correct to 3 decimal places. iii) Another approximation to fe"dx is to be calculated by using two trapezium of unequal width. The first trapezium has width h and the second trapezium has width (1 – h), so that the three ordinates are at x= 0, x=h and x=1. Show that the total area Tof these two trapezium is given by T = - iv) Show that the value of h for which T is a minimum is given by h = In
Transcribed Image Text:а) Use i) Simpson's rule with four segment, and ii) Simpson's rule to obtain the integration of: f(x) = 0.2+ 25x – 200.x² + 675x – 900x* + 400.x from a = 0 to b 0.8. b) The trapezium rule, with 2 intervals of equal width, is to be used to find an approximate value for [e"dx. i) Explain with the aid of a sketch, why the approximation will be greater than the exact value of the integral. ii) Calculate the approximate value and the exact value, giving each answer correct to 3 decimal places. iii) Another approximation to fe"dx is to be calculated by using two trapezium of unequal width. The first trapezium has width h and the second trapezium has width (1 – h), so that the three ordinates are at x= 0, x=h and x=1. Show that the total area Tof these two trapezium is given by T = - iv) Show that the value of h for which T is a minimum is given by h = In
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