public void DIntegralTestx2_1to2()
{
// p(x) = x^2
// ∫_1^2(x^2dx) == [x^3/3]_{x=1}^2 = (8-1)/3 = 7/3
var p = new RealPolynomial(new double[] { 0, 0, 1 });
double r = p.Integral(1, 2);
Assert.IsTrue(IsSimilar(r, 7.0 / 3.0));
}
public void DIntegralTestx3px2_2to5()
{
// p(x) = x^3 + x^2
// ∫_2^5(x^3+x^2)dx == [x^4/4+x^3/3]_{x=2}^5 = 765/4
var p = new RealPolynomial(new double[] { 0, 0, 1, 1 });
double r = p.Integral(2, 5);
Assert.IsTrue(IsSimilar(r, 765.0 / 4.0));
}
public void DIntegralTestx2_0to1()
{
// p(x) = x^2
// ∫_0^1(x^2dx) == [x^3/3]_{x=0}^1 = 1/3
var p = new RealPolynomial(new double[] { 0, 0, 1 });
double r = p.Integral(0, 1);
Assert.IsTrue(IsSimilar(r, 1.0 / 3.0));
}
public void DIntegralTestx_0to1()
{
// p(x) = x
// ∫_0^1(xdx) == [x^2/2]_{x=0}^1 = 1/2
var p = new RealPolynomial(new double[] { 0, 1 });
double r = p.Integral(0, 1);
Assert.IsTrue(IsSimilar(r, 1.0 / 2.0));
}
public void DIntegralTestx_1to2()
{
// p(x) = x
// ∫_1^2(xdx) == [x^2/2]_{x=1}^2 = (4-1)/2 = 3/2
var p = new RealPolynomial(new double[] { 0, 1 });
double r = p.Integral(1, 2);
Assert.IsTrue(IsSimilar(r, 3.0 / 2.0));
}
public void DIntegralTest2_4to3()
{
// p(x) = 2
// ∫_4^3(2dx) == [2x]_{x=4}^3 = (6-8) = -2
var p = new RealPolynomial(new double[] { 2 });
double r = p.Integral(4, 3);
Assert.IsTrue(IsSimilar(r, -2.0));
}
public void DIntegralTest2_3to4()
{
// p(x) = 2
// ∫_3^4(2dx) == [2x]_{x=3}^4 = (8-6) = 2
var p = new RealPolynomial(new double[] { 2 });
double r = p.Integral(3, 4);
Assert.IsTrue(IsSimilar(r, 2.0));
}
public void IIntegralTestx()
{
// p(x) = x
// ∫xdx == [x^2/2] +C
double C = 1.0;
var p = new RealPolynomial(new double[] { 0, 1 });
var pI = new RealPolynomial(new double[] { C, 0, 1.0 / 2.0 });
var r = p.Integral(C);
Assert.IsTrue(IsSimilar(r, pI));
}
public void IIntegralTest2()
{
// p(x) = 2
// ∫(2)dx == [2x] +C
double C = 1.0;
var p = new RealPolynomial(new double[] { 2 });
var pI = new RealPolynomial(new double[] { C, 2 });
var r = p.Integral(C);
Assert.IsTrue(IsSimilar(r, pI));
}