Definite integral between 0 and 0.5 of sin(x) / x cannot be computed

[Former user]

the definite integral between 0 and 0.5 of sin(x) / x cannot be computed ... returns NaN rather than 0.4931 ... checked cos(x) / x and it's the same problem, also returning NaN ... the indefinite integral works fine ... sin(x) / x gives Si(x) and cos(x) / x gives Ci(x)

[Axel Kramer]

Commited: https://bitbucket.org/axelclk/symja_android_library/commits/388c3eb4562d27a58a2a0c4d51187ded472d1551

[Tony Admin]

have tried the symja-mini-2015-03-23.jar but am still get NaN

[Axel Kramer]

Do you have a snippet to demonstrate the problem? Do you use the org/matheclipse/core/reflection/system/Integrate.java to calculate the integral?

I tested this calls:

Integrate(sin(x) / x, {x,0,0.5})
Integrate(cos(x) / x, {x,0.25,0.5})

[Tony Admin]

we are importing org.matheclipse.core.eval.MathUtils and then using the MathUtils.integrate(String function, String x, String lower, String upper) function as follows:

MathUtils.integrate(sin(x), x, 0, 0.5) returns 0.12241743810962748 MathUtils.integrate(sin(x)x, x, 0, 0.5) returns 0.0406342576590166 MathUtils.integrate(sin(x)/2x, x, 0, 0.5) returns 0.0203171288295083 MathUtils.integrate(sin(x)/x, x, 0, 0.5) returns NaN MathUtils.integrate(x^2/x, x, 0, 0.5) returns NaN

is there a better way?

[Axel Kramer]

OK, I switched from Romberg method for numerical integration to the better suited LegendreGauss method.

Call with LegendreGauss as defaut method:

MathUtils.integrate("sin(x)/2*x", "x", "0", "0.5");

or select one of the methods: LegendreGauss, Simpson, Romberg, Trapezoid

MathUtils.integrate("LegendreGauss", "sin(x)/2*x", "x", "0", "0.5");

See commit: https://bitbucket.org/axelclk/symja_android_library/commits/385d590e7998478577804c19737352dddde6bbb6

[Tony Admin]

thanks, that's great ... compiled the 3 revised files and added them into the symja-2015-03-23 jar (replacing the old class files) and then tested in the app ... all works well ... will you be uploading an updated symja-mini version of the jar?

[Axel Kramer]

Uploaded symja-mini jar

[Tony Admin]

thanks again!