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Integration Introduction

Integration is the process of finding the area under a graph. It is the reverse process to differentiation, and has wide applications like finding areas under curves and volumes of solids. It is an important concept in mathematics and is one of the operations in calculus.

Basic formulas for Integration:

Most of the following basic formulas directly follow the differentiation rules.

Basic formulas for Integration

Example for Integration:

Example for Integration

Definite Integrals:

The definite integral of a function is closely related to the antiderivative and indefinite integral of a function. The primary difference is that the indefinite integral, if it exists, is a real number value, while the latter two represent an infinite number of functions that differ only by a constant.

Properties of definite integrals:

Certain properties are useful in solving problems requiring the application of the definite integral. Some of the more common properties are

Properties of definite integrals

Following are the topics covered in Integration.

  • Integration by Parts
  • Integrals Involving Trig Functions
  • Trig Substitutions
  • Partial Fractions
  • Integrals Involving Roots
  • Integrals Involving Quadratics
  • Integration Strategy
  • Improper Integrals
  • Comparison Test for Improper Integrals
  • Approximating Definite Integrals