Question

For Questions below. write computer code in any programming language or mathematical software to estimate dz using the given method. Then calculate the absolute and relative errors for each. Use exact value p 0.6044 戰,omposite Trapezoidal Rule with N = 6.

Please Write in C programming Language

Answer 1

`Hey,

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#include<stdio.h>
#include<math.h>
// A sample function whose definite integral's
// approximate value is computed using Trapezoidal
// rule
float y(float x)
{
// Declaring the function f(x) = 1/(1+x*x)
return (1.0/ sqrt(x*x -4.0));
}

// Function to evalute the value of integral
float trapezoidal(float a, float b, float n)
{
// Grid spacing
float h = (b-a)/n;
int i;
// Computing sum of first and last terms
// in above formula
float s = y(a)+y(b);

// Adding middle terms in above formula
for ( i = 1; i < n; i++)
s += 2*y(a+i*h);

// h/2 indicates (b-a)/2n. Multiplying h/2
// with s.
return (h/2)*s;
}

// Driver program to test above function
int main()
{
// Range of definite integral
float x0 = 3;
float xn = 5;

// Number of grids. Higher value means
// more accuracy
int n = 6;
float I=trapezoidal(x0, xn, n);
printf("Approximation is %f\nAbsolute Error is %f\nRelative error is %f\n",I,fabs(I-0.6044),fabs(I-0.6044)/0.6044);

return 0;
}

FAcheckimain.exe Approximation is 0.686364 Absolute Error is 0.001964 Relative error is θ.ee3249 Process returned θ (8x8) execution time : 0.277 s Press any key to continue ENG 1248 PM IN 05/11/19 O Type here to search

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