Cavalieri's Quadrature Formula

Author

Eric W. Weisstein
April 14, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/CavalierisQuadratureFormula.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/CavalierisQuadratureFormula.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Formula

v4.2

Integrate[x^n,{x,a,b}]

Integrate[x^n,{x,a,b},Assumptions->n==-1]

Integrate[x^n,{x,a,b},Assumptions->x∈Reals]

v5.0

Integrate[x^n,{x,a,b}]//Timing

FullSimplify[Integrate[x^n,{x,a,b}],(x|a|b)∈Reals]//Timing

Integrate[x^n,{x,a,b},Assumptions->(a|b)∈Reals]

Integrate[x^-1,{x,a,b},Assumptions->(a|b)∈Reals]//Timing

Integrate[x^n,{x,a,b},Assumptions->x∈Reals]//Timing

Integrate[x^n,{x,a,b},Assumptions->n==-1]//Timing

v6.0

Integrate[x^n,{x,a,b}]//Timing

Integrate[x^n,{x,a,b},Assumptions->(a|b)∈Reals]

Integrate[x^-1,{x,a,b},Assumptions->(a|b)∈Reals]//Timing

FullSimplify[Integrate[x^n,{x,a,b}],(x|a|b)∈Reals]//Timing

Integrate[x^n,{x,a,b},Assumptions->x∈Reals]//Timing

Integrate[x^n,{x,a,b},Assumptions->n==-1]//Timing