Question

• Create two vectors with entries evenly spaced between 0 and pi. One vector should be of length 100 and the other should be of length 1000. Then apply these vectors to the function sin(2x).
• Now use cumsum and cumtrapz to approximate the integral of sin(2x). Do this for both lengths as before.
• Subtract 0.5 from every element of each integral vector to center their graphs at 0. Then compare the computed vectors with the analytic antiderivative as before. Return the magnitude of the max error for each of the four cases.
• Plot the best approximation for the integral. Add a title to the plot

Answer 1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc%clears screen
clear all%clears history
close all%closes all files
x1=linspace(0,pi,100);
x2=linspace(0,pi,1000);
y1=sin(2*x1);
y2=sin(2*x2);
Ia1=2*cos(2*x1);
Ia2=2*cos(2*x1);
disp('Integral for first');
I1=cumtrapz(x1,y1)
disp('Integral for second');
I2=cumtrapz(x2,y2)
disp('Max error is first is');
max(abs(I1(:)-Ia1(:)))
disp('Max error is second is');
max(abs(I2(:)-Ia2(:)))
plot(x2,I2);
title('Plot for 1000 points');

Kindly revert for any queries

Thanks.