b)The trapezium rule, with 2 intervals of equal width, is to be used to find an approximatevalue for fe"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.i11)Another approximation to'e*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– k), so that the three ordinates are at x= 0, x=h and x=1. Show that the totalarea T of these two trapezium is given by T =(e-1 + h(1- e-) + ei ).(e)Show that the value of h for which T is a minimum is given by h = Iniv)

Answered: Image /qna-images/answer/aa66de78-cc22-4c5a-ab76-3150319ab40b.jpg

The trapezium rule, with 2 intervals of equal width, is to be used to find an approximate value for fe"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. ii1) Another approximation to 'e*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– k), so that the three ordinates are at x= 0, x=h and x=1. Show that the total area T of these two trapezium is given by 7 =(r! + h(1- e*1) + e* ). iv) Show that the value of h for which T is a minimum is given by h = In'

The trapezium rule, with 2 intervals of equal width, is to be used to find an approximate value for fe"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. ii1) Another approximation to 'edx is to be calculated by using two trapezium of unequal width. The first trapezium has width h and the second trapezium has width (1– k), so that the three ordinates are at x= 0, x=h and x=1. Show that the total area T of these two trapezium is given by 7 =(r! + h(1- e1) + e* ). iv) Show that the value of h for which T is a minimum is given by h = In'

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids

Section: Chapter Questions

Problem 79A

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