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.
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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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F428963f8-cefb-4cab-8cd7-ba0d567dcebf%2Fa5505598-b170-4be6-be23-4573975a18d1%2Fdz3dmd6_processed.png&w=3840&q=75)
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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