apcalcIntegrals

Integrals **Integration is an important concept in mathematics and, together with differentiation, is one of the two main operations in calculus. **  ﻿ ﻿  **What is an integral? ** There are two types of integrals, a [|definite integrals] and [|indefinite integrals]. A definite integral can be interpreted as an area or a generalization of an area under the curve of a function that is bounded by two points and the x or y axis. an indefinite integral has no upper or lower limits therefore it is known as an [|antiderivitive] ﻿Integration can be traced as far back as ancient Egypt 1800 BC. The first documented technique capable of determining integrals is the method of exhaustion by the ancient greek astronomer [|Eudoxus of Cnidus](370 BC), which sought to find areas and volumes by breaking them up into an infinite number of shapes for which the area or volume was known.    The major advance in integration came in the 17th century with the independent discovery of the [|fundamental theorem of calculus] by [|Isaac Newton] and [|Gottfried Leibniz]. The theorem demonstrates a connection between integration and differentiation. Integration was first rigorously formalized, using limits, by [|Riemann]. The equation we now know as [|Riemann sums]. This is the most common way you will see a definite integral equation. The ∫ sign represents integration; //a// and //b// are the //lower limit// and //upper limit//, respectively, of integration, defining the domain of integration; and the f(x) represents the equation of the graph as it varies over the interval of [a,b]; and //dx// is the [|variable of integration].
 * Where did integration come from? **
 * What does an integral look like?**

**Helpful things to know when solving:** **Definite integrals** **Indefinite integrals**

**Indefinite integrals of trig functions** 

﻿media type="custom" key="9652892" align="left"
 * How to solve definite integrals **

**How to solve indefinite integrals** media type="youtube" key="VoHjgLNChZE" height="349" width="425"


 * Different methods of integration **
 * [|1. The General Power Formula]
 * [|2. The Basic Logarithmic Form]
 * [|3. The Exponential Form]
 * [|4. The Basic Trigonometric Forms]
 * [|5. Other Trigonometric Forms]
 * [|6. Inverse Trigonometric Forms]
 * [|7. Integration by Parts]
 * [|8. Integration by Trigonometric Substitution]
 * [|9. Integration by Use of Tables]
 * [|Table of Common Integrals]
 * [|10. Integration by Reduction Formulae]
 * [|11. Integration by Partial Fractions]

<span style="color: #3186d3; font-family: Arial,Helvetica,sans-serif; font-size: 150%;">**Work Cited** [] [] [] [] [] [] []