ANSWER PLZ A AND B а)Usei)Simpson'srule with four segment, andii)Simpson'sruleto obtain the integration of:f(x) = 0.2+ 25x – 200.x² + 675x – 900x* + 400.xfrom a = 0 to b 0.8.b)The trapezium rule, with 2 intervals of equal width, is to be used to find an approximatevalue for [e"dx.i)Explain with the aid of a sketch, why the approximation will be greater than theexact value of the integral.ii)Calculate the approximate value and the exact value, giving each answer correct to3 decimal places.iii)Another approximation to fe"dx is to be calculated by using two trapezium ofunequal 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 totalarea 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

Name: ANSWER PLZ A AND B а)Usei)Simpson'srule with four segment, andii)Simps
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Description: ANSWER PLZ A AND B а)Usei)Simpson'srule with four segment, andii)Simpson'sruleto obtain the integration of:f(x) = 0.2+ 25x – 200.x² + 675x – 900x* + 400.xfrom a = 0 to b 0.8.b)The trapezium rule, with 2 intervals of equal width, is to be used to find

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a) Use i) 73 rule with four segment, and ii) Simpson's rule 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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Topic Video

Question

ANSWER PLZ A AND B

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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