Question

For the integral below, write a program to do the trapezoid rule using the sequence of mesh sizes h = (b – a)/2, (b – a)/4, (b – a)/8, ..., (b – a)/128, where b – a is the length of the given interval: f(x) = e−x sin(4x), [0, pi], I(f) = (4/17)(1 − e^-pi) = 0.2251261368. Verify that the expected rate of error decrease is obtained. Attach your code and a plot of error vs. h.

Answer 1

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We write the C-Program using Function. We define a function where .

The code is as follows:

#include<stdio.h>

#include<math.h>

main()

{

int n,i;

float a,b,h,x,sum=0,int;

printf("Enter the number of subintervals");

scanf("%d",&n);

printf("Enter the lower limit of the integral");

scanf("%f",&a);

printf("Enter the upper limit of the integral");

scanf("%f",&b);

h=fabs(a-b)/n;

for(i=1,i<n;i++)

x=a+i*h;

sum+=f(x);

}

int=(0.5)*h*(f(a)+f(b)+2*sum);

printf("the integral is %f",int);

}

float f(float x)

{

return exp(-x)*sin(4*x);

}

Plot of error vs h:

Considering

we get the following graph: