The Table Of Integrals

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    A compilation of the fundamental integrals with their derivations and examples.

GO TO: Prologue

GO TO: The Fundamentals of Integration

GO TO: Lebesgue Integration

GO TO: A Minor Caution with the Chain Rule

GO TO: The Fundamental Theorem of The Calculus

Fundamental Forms

GO TO:      Kinetic Energy, Work done by Gravity
GO TO:    Diminution of Radioactivity
GO TO:  Entropy
GO TO:  


Algebraic Forms

GO TO: Entropy of Heated Ideal Solid
GO TO: Spectral Density of Blackbody Radiation
GO TO: Relativistic Astrogation
GO TO: Witch of Agnesi: Point Source Illumination of Moving Sphere
GO TO: Direct Gravitational Deflection of Starlight
GO TO: Revisited Electric Field of Infinitely Long Wire
GO TO: Gravitational Refraction of Starlight
GO TO: Revisited The Catenary
GO TO:   Oscillation Period of Mass on a Spring
GO TO:    Angle Traversed on an Orbit
GO TO: Time Elapsed on an Orbit
GO TO: Stirling's Formula
GO TO: See
GO TO: Timing a Free Falling Body
GO TO:  


Trigonometric Forms

GO TO: Solar Heating of a Flat Plate
GO TO: Kinetic Energy of a Mass on a Spring
GO TO: Electrical Energy from Alternating Current
GO TO:    Volume Contained in a Cylindrical Intersection
GO TO: Energy Dissipated by a Skidding Wheel
GO TO:    Average Radius of an Elliptical Orbit
GO TO: Area of an Orbital Segment
GO TO: Angular Momentum of a Thin Spherical Shell
GO TO:   Volume of a Tubular Intersection


Exponential Forms

GO TO: Resource Depletion
GO TO: Free Energy in a Boson Gas


Definite Integrals

GO TO:  The Stefan-Boltzmann Law
GO TO: Gaussian Probability (The Maxwell Distribution)
GO TO: The Gaussian Wave Packet

Loop Integrals

(integration on the complex plane)

GO TO: Cauchy's Integral Theorem

GO TO: Integrating a Function with a removable Singularity

                                                                Radio Polarization of a Ferroelectric

GO TO: Singularities and Their Residues

GO TO: Integrating a Function with Multiple Simple Poles

GO TO: Integrating a Function with Poles

GO TO: Residues of the Dirac Delta



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