Write a C program ( Care should be taken not to use extensions of C + + language

Question

Write a C program (Care should be taken not to use extensions of C + + language in your work) that reads two real terminals (a, b) representing the integration of a definite integral terminals. The program's goal is to compare four different methods of numerical integration. Each method will be programmed by a different function. Here is each method:

Method of rectangles :       (int_{x_{m}}^{x_{n}} f(x)dx pprox hsum_{i=0}^{n-1} f(x_{i}))   

The midpoint method :        (int_{x_{m}}^{x_{n}} f(x)dx pprox hsum_{i=0}^{n-1} f(x_{i+1/2}))   

Method of trapezoids :       (int_{x_{m}}^{x_{n}} f(x)dx pprox h((( f(x_{m}) +f(x_{n}))/2) + sum_{i=1}^{n-1} f(x_{i})))   

SImpson method :      (int_{x_{m}}^{x_{n}} f(x)dx pprox h/3( f(x_{0}) + 2 sum_{i=1}^{n/2-1} f(x_{2i}) +4 sum_{i=1}^{n/2} f(x_{2i-1}) + f(x_{n})))   

Here is an example of the results of the program with terminals 0 and 1:

Enter terminals : 0 1

Exact value : 1.71828182845905

Method    intervals    approximated value            error

Rectangle    20      1.67568274321374 2.479168 %

Midpoint                         20    1.71810285381891    0.010416 %

Trapeze 20 1.71863978892522    0.020832 %

Simpson                        20     1.71828188810386          0.000003 %

Rectangle 40     1.69689279851633            1.244792 %

Midpoint              40 1.71823708235212    0.002604 %

Trapeze                       40 1.71837132137206    0.005208 %

Simpson    40       1.71828183218768    0.000000 %

Rectangle     60 1.70400258808007 0.831019 %

Midpoint    60     1.71826194109901 0.001157 %

Trapeze 60         1.71832160331723 0.002315 %

Simpson    60 1.71828182919560 0.000000 %etc. .

Note: Use the double type in your calculations.

Note: Use the following conversion specifications : % 8d for the 2nd column %19.14f for the 3rd column and %10.6lf for the 4th column.

Data for submission : Here are four pairs of real that you must use to produce the results of the program:0 1, -1 0, -1 1, -1.5 1.5

Explanation / Answer

#include #include double f(double x) { return exp(x); }double integral_by_rectangle(double (*f)(double), double a, double b, int n);double integral_by_midpoint(double (*f)(double), double a, double b, int n);double integral_by_trapeze(double (*f)(double), double a, double b, int n);double integral_by_simpson(double (*f)(double), double a, double b, int n);int main(){ const char* labels[] = { "Rectangle", "Midpoint", "Trapeze", "Simpson" }; double (*integrals[4])(double(*)(double), double, double, int) = { integral_by_rectangle, integral_by_midpoint, integral_by_trapeze, integral_by_simpson }; double a, b, Ie, In, err; int n, i; printf("Enter intervals: "); scanf("%lf%lf", &a, &b); Ie = f(b) - f(a); printf("Exact value: %.15f ", Ie); puts("Method intervals approximated value error"); for (n = 20; n < 101; n += 20) { for (i = 0; i < 4; ++i) { In = integrals[i](f, a, b, n); err = 100.0 * fabs(In - Ie) / Ie; printf("%-9s %8d %19.14f %10.6lf%% ", labels[i], n, In, err); } } return 0;}double integral_by_rectangle(double (*f)(double), double a, double b, int n){ double h = (b-a) / n; double x = a, sum = 0; int i; for (i = 0; i

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