Homework 15 Solution

Homework 15 Solution - Lecture 15 MEEN 357 Homework...

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Lecture 15 MEEN 357 Homework Solution 1 Lecture-15-Homework-Solution-2009.doc RMB 1. Problem 17.2 of the textbook. This problem should be turned in, as usual, at the start of class. Solution: You are to evaluate the integral ( ) 4 2 0 1 x I ed x =− (15.1) a) Analytically b) Single application of trapezoidal rule. c) Composite trapezoidal rule with 2 N = and 4 N = . d) Single application of Simpson’s 1/3 rule. e) Composite Simpson’s 1/3 rule with 4 N = . f) Simpson’s 3/8 rule. The book does not specify a single application of the 3/8 rule. For simplicity, we shall work the single application case. You are asked to determine the percent relative error for parts b) through f) based upon the answer to part a). Part a) Exact The integral of () 2 1 x f xe is elementary and is given by 22 1 1 2 xx x x e C −− =+ + (15.2) Therefore, 4 4 228 8 0 0 11 1 7 1 14 2 2 2 3.5002 x a x I e e e = −−− = ⎛⎞ = = + −=+ ⎜⎟ ⎝⎠ = (15.3) Part b) Single application of trapezoidal rule The formula for the approximate integral is ( ) ( ) 2 b f af b Ib a + (15.4) Since ( ) ( ) () () 00 4 .9997 fa f fb f == (15.5) it follows from (15.4) that
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Lecture 15 MEEN 357 Homework Solution 2 Lecture-15-Homework-Solution-2009.doc RMB () ( ) ( ) 0 .9997
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Homework 15 Solution - Lecture 15 MEEN 357 Homework...

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