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Subsections

# Integration

## Abs-Exp

Origin:Quateroni A, Sacco, R. and Saleri, F., Numerical mathematics, Springer 2000, pp. 413

Compute

The result is a range with width lower than that includes the value of the integral.

Method: IntegrateRectangle or IntegrateTaylor
Solutions::[1.2642411126774618, 1.2642411226375476] (
Computation time (February 2006):

 DELL D400 (1.7Ghz) 0.019s (Rectangle) 0.004 (Taylor)

## comp.soft-sys.math.maple18257

Origin: Article 18257 of comp.soft-sys.math.maple

Compute

Method: IntegrateTaylor
Solution: [6.2831848095217104, 6.2831858068365776] (
Solution:[6.2831853021819217, 6.2831853121792607] (
Computation time (Mars 2006):
 DELL D400 (1.7Ghz), Taylor order: 3 0.22s (), 1.35s () DELL D400 (1.7Ghz), Taylor order: 4 0.09s (), 0.21s () DELL D400 (1.7Ghz), Taylor order: 5 0.09s (), 0.18s () DELL D400 (1.7Ghz), Taylor order: 6 0.07s (), 0.18s ()

## Ellipsoid

Origin:Quateroni A, Sacco, R. and Saleri, F., Numerical mathematics, Springer 2000, pp. 410-412

Compute

The result is a range with width lower than that includes the value of the integral.

Method: IntegrateRectangle
Solution: [.081356291802596431, .081357224879917173] ()
Solution: [0.081356786414213011, 0.081356796338971332] ()
Computation time (February 2006):

 DELL D400 (1.7Ghz) 0.001s (), 0.002s ()

## Sail boat

Origin:Quateroni A, Sacco, R. and Saleri, F., Numerical mathematics, Springer 2000, pp. 410-412

Compute

with , , . The result is a range with width lower than that includes the value of the integral.

Method: IntegrateRectangle
Solution: [100.06136781918083, 100.06136881760561] (
Solution:[100.06136831296580, 100.06136832296060] (
Computation time (February 2006):

 DELL D400 (1.7Ghz) 0.0457s (), 0.886s ()

## sci.math.num-analysis89520

Origin: Article 89520 of sci.math.num-analysis

Compute

Method: IntegrateTaylor
Solution: [1.99999527,2.0000004987] (
Solution:[1.999999995087,2.0000000050096] (
Computation time (Mars 2006):
 DELL D400 (1.7Ghz) 0.62s (), 1.33s ()

## sci.math.num-analysis.91892

Origin: Article 91892 of sci.math.num-analysis
with


k = 400 * Pi / 3
a = 3.75E-6
q = 0.000875
d1 = k*R * (3*a^2 - 2*R^2)
d2 = 2*R^2 + a^2 * (k^2 * R^2 - 3)
R = sqrt(a^2 + (q-z)^2)
P = 0.005 / (0.17708 * 8*Pi^2*R^5

Compute

Method: IntegrateTaylor
Solution: [886.6380446722454,886.6380456712287] (
Method: IntegrateTaylor at order
Computation time (August 2006):
 DELL D400 (1.7Ghz) 164.24s () 71.28s ()

## stoutemyer2007

Origin: [12]

Compute

Method: IntegrateTaylor
Solution: [0.67637670822541165607681348942, 0.67637670822543264594435536661], (
Method: IntegrateTaylor at order for in and Integrate for in
Computation time (November 2007):
 DELL D620 (1.7Ghz) 11s

Next: Other problems: inequalities, parametric Up: benches Previous: Optimization
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