3.24) my professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text. Numerical methods for evaluating definite integrals1dx5.24.Evaluatez approximately, using (a) the trapezodial rule, and (b) Simpson's rule, where the interval.21+ x[0, 1] is divided into n = 4 equal parts.Let f(x) = 1/(1 + x²). Using the notation on Page 104, we find Ar = (b – a)/n = (1 – 0)/4 = 0.25. Then,keeping four decimal places, we have yo = f(0) = 1.0000, y = f(0.25) = 0.9412, y2 = f(0.50) = 0.8000, y3 =f(0.75) = 0.6400, and y, = f(1) = 0.50000.%3D%3D(a) The trapezoidal rule givesAr{Yo +2y, + 2y, + 2y; + y4} =20.25{1.0000 + 2(0.9412)+ 2(0.8000) + 2(0.6400) + 0.500}= 0.7828.(b) Simpson's rule givesAr· {Yy, + 4y, + 2y, + 4y, + y,} =30.25{1.0000 + 4(0.9412) + 2(0.8000) + 4(0.6400) + 0.500}2= 0.7854.The true value is t/4 - 0.7854.

We need to evaluate ∫01dx1+x2 , here a=0 , b=1 , f(x) = 11+x2 We need to divide the interval in 4…

Answered: Evaluate | dx approximately, using (a)…

Evaluate | dx approximately, using (a) the trapezodial rule, and (b) Simpson's rule, where the interval '1+x² [0, 1] is divided into n = 4 equal parts.

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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