Question

PLEASE use MATLAB only to write the code

100 10 Assume -18.79829683678703 is the "exact" value of the integral. Estimate this integral by the composite trapezoid rule with 3, 5, and 7 points. Calculate the percent difference from the exact value in each case using PD-100 abs(exact-trap)Vexact)

Answer 1

clear
clc

f = @(x) (100./x).*sin(10./x);

a = 1; b=3;
n3 = 3; n5 = 5; n7 = 7;

f_exact = -18.79829683678703;

step3 = (b-a)/n3;
step5 = (b-a)/n5;
step7 = (b-a)/n7;

% dx = step
% I = ((b-a)/2n)*(f(a)+ f(a+dx) + ... + f(b-dx)+ f(b) )

I3 = 0;
for j=a:step3:b % a:dx:b
I3 = I3 + ((b-a)/(2*n3))*f(j);
end

I5 = 0;
for j=a:step5:b
I5 = I5 + ((b-a)/(2*n5))*f(j);
end

I7 = 0;
for j=a:step7:b
I7 = I7 + ((b-a)/(2*n7))*f(j);
end

integration_n3 = I3
percent_err_n3 = 100*abs((f_exact - I3)/f_exact)

integration_n5 = I5
percent_err_n5 = 100*abs((f_exact - I5)/f_exact)

integration_n7 = I7
percent_err_n7 = 100*abs((f_exact - I7)/f_exact)

integration n3 -38. 8447 percent err n3 106.6396 integration n5- -22.6645 percenterrn5 = - - 20.5666 integration n7 = -17.1383 percent_err n7 8.8306

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