Cody

# Problem 1197. Numerical Integration

Solution 190034

Submitted on 12 Jan 2013 by Richard Zapor
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### Test Suite

Test Status Code Input and Output
1   Pass
%% x0 = 1; I_correct = 2.6405789412796; fprintf('Relative difference to reference solution: %e\n',norm(coshint(x0)-I_correct)/I_correct) assert(norm(coshint(x0)-I_correct)/I_correct <= 1e-10)

```Relative difference to reference solution: 5.839165e-13 ```

2   Pass
%% x0 = 2; I_correct = 3.9464053536380; fprintf('Relative difference to reference solution: %e\n',norm(coshint(x0)-I_correct)/I_correct) assert(norm(coshint(x0)-I_correct)/I_correct <= 1e-10)

```Relative difference to reference solution: 1.905134e-13 ```

3   Pass
%% x0 = 13; I_correct = 9.4065231838369e+02; fprintf('Relative difference to reference solution: %e\n',norm(coshint(x0)-I_correct)/I_correct) assert(norm(coshint(x0)-I_correct)/I_correct <= 1e-10)

```Relative difference to reference solution: 5.644142e-14 ```

4   Pass
%% randomized test for small values of x0 where % cosh(x) ~ 1 + x^2/2 + ... % and up to x0=1e-5 Integrating (analytically) the approximation is % accurate enough for l=1:5 x0 = 1e-6 * (1+rand); I_correct = pi*(4+x0^2)/4/sqrt(2); fprintf('Relative difference to reference solution: %e\n',norm(coshint(x0)-I_correct)/I_correct) assert(norm(coshint(x0)-I_correct)/I_correct <= 1e-10) end

```Relative difference to reference solution: 5.115707e-13 Relative difference to reference solution: 5.833385e-13 Relative difference to reference solution: 1.479337e-14 Relative difference to reference solution: 7.356702e-14 Relative difference to reference solution: 1.769207e-13 ```