Question

Problem 6. Consider the definite integral fo, sin(VE) cos( dz. Use n-100 and n = 300 separately, to find the Riemann sum for this integral. Keep at least four decimal places for your answer
please explain and do in matlab

Answer 1

MATLAB Code:

close all
clear
clc

a = 0; b = pi; % integration limits

%% n = 100
n = 100;
func = @(x) sin(sqrt(x)) .* cos(sqrt(x)); % input function

h = (b - a)/n;
I = h*sum(func(a + h/2:h:b-h/2)); % Riemann sum using midpoint rule

fprintf('Riemann Sum (n = %4d): %.6f\n', n, I)

%% n = 300
n = 300;
func = @(x) sin(sqrt(x)) .* cos(sqrt(x)); % input function

h = (b - a)/n;
I = h*sum(func(a + h/2:h:b-h/2)); % Riemann sum using midpoint rule

fprintf('Riemann Sum (n = %4d): %.6f\n', n, I)

Output:

Riemann Sum (n = 100): 0.717351
Riemann Sum (n = 300): 0.717069