The Table Of Integrals

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

GO TO:

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