Sine Power Integral

Evaluates the sine power integral.

Controller: CodeCogs

Contents

Interface
Sine Power Integral
Page Comments

Interface

C++

Excel

Sine Power Integral

doublesine_power_integral(	double	`a`
	double	`b`
	int	`n`	)

This function evaluates the sine power integral with given parameters, defined by

$\mathrm{sinepower}(a, b, n) = \int_a^b \sin(t)^n \mathrm{d}t$

(2)

The algorithm uses the fact that

$\int \sin^n(t) \mathrm{d}t = \frac{1}{n} \left( \sin^{n-1}(t) \cos(t) + (n-1) \int \sin^{n-2}(t) \mathrm{d}t \right)$

(3)

Example 1

#include <codecogs/maths/special/sine_power_integral.h>
#include <iostream>
#include <iomanip>
 
int main()
{
  std::cout << std::setprecision(10);
  std::cout << "For lower and upper bounds a = 0 and b = 10, " << std::endl;
  std::cout << "and 0 <= n < 10, the value of the integral is" << std::endl;
  for (int n = 0; n < 10; n++)
  {
    std::cout << "n = " << n << " : ";
    std::cout << Maths::Special::sine_power_integral(0, 10, n) << std::endl;
  }
  return 0;
}

Output

For lower and upper bounds a = 0 and b = 10,
and 0 <= n < 10, the value of the integral is
n = 0 : 10
n = 1 : 1.839071529
n = 2 : 4.771763687
n = 3 : 1.308824601
n = 4 : 3.545048474
n = 5 : 1.061758823
n = 6 : 2.947543192
n = 7 : 0.913186379
n = 8 : 2.577621119
n = 9 : 0.8124365163

References

John Burkardt's library of statistical C++ routines, http://www.csit.fsu.edu/~burkardt/cpp_src/prob/prob.html

Parameters

a	the lower limit of integration
b	the upper limit of integration
n	the power of the sine function

Returns

An approximation of the sine power integral.

Authors

Lucian Bentea (September 2005)

Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

Not a member, then Register with CodeCogs. Already a Member, then Login.