void test_integration(void) {
function_t *f = function_create("2**x - log(x)");
ASSERT_EQ(integrate_simpson(f, 0.5, 2.3), 4.60212);
function_destroy(f);
f = function_create("1/x - sin(x)**3");
ASSERT_EQ(integrate_simpson(f, 2.45, 8.145), 1.54018);
function_destroy(f);
}
void problem1() {
int k = 0;
double integral = 0;
double step = 0;
double step_old;
FILE *fp = fopen("out-1a.txt", "w");
fprintf(fp, "#%4s %5s %15s %15s\n", "k", "n", "step", "integral");
do {
int n = 2;
do {
step_old = step;
step = integrate_simpson(f1, 100 * k, 100 * (k+1), n);
n *= 2;
fprintf(fp, "%5i %5i %15g %15g\n", k, n, step, integral);
} while (fabs(step - step_old) > 1e-10);
integral += step;
k++;
} while (fabs(step) >= 1e-5);
fclose(fp);
}