Mathematical Foundations · Integral Calculus

Integral Calculus · Integrals Depending on a Parameter

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Advanced mathematical analysis · Integral calculus

Overview

Topics covered

  • Introduction
  • Integrals dependent on a parameter
  • Introduction and problem statement
  • Continuity of the integral function
  • Derivability and integration under the integral sign (Leibniz's Rule)
  • Extension: Variable integration limits

Related concepts

Main connections

  • Calculus & differentiation
  • Normal (Gaussian) distribution
  • Mathematical expectation & moments
  • Linear algebra & matrices

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

I(y)=∫abf(x,y)dx.
View LaTeX sourceI(y) = \int_{a}^{b} f(x,y) \dd x.