## Integral Definition:

A numerical value:
Area under the graph of a
function for some interval.

## Limit of a Function Notation:

The limit of a function ƒ(x) is L as L approaches a

limx → a ƒ(x) = L

## Integral Notation:

∫ƒ(x) dx.
integral of f of x dx.

## Integral of a constant rule:

Integral of a constant n is
nx + C.
ƒ(x) = 6, then ∫ƒ(x) = 6x + C

## Integral power rule:

ƒ(x) = xn, then ∫ƒ(x)dx is:
 xn + 1 n + 1

## Integral power rule example:

ƒ(x) = x2
Using the power rule with n = 2
∫ƒ(x) = x2 + 1/(2 + 1) = x3/3

## Trigonometric Integrals

ƒ(x)ƒ'(x)Domain
sin(x)-cos(x)-∞ < x < ∞
cos(x)sin(x)-∞ < x < ∞
tan(x)-Ln cos(x)x ≠ π/2 + πn, n ∈ Ζ
csc(x)Ln(csc(x) - cot(x))x ≠ πn, n ∈ Ζ
sec(x)Ln(sec(x) - tan(x))x ≠ π/2 + πn, n ∈ Ζ
cot(x)Ln sin(x)x ≠ πn, n ∈ Ζ

## Logarithmic Integrals

ƒ(x)ƒ'(x)
exex
axax/Ln(a) where a > 0, a ≠ 1
Ln(x)1/x
logaxx * Ln(x) - x

## Integral Calculator:

For more help on integrals

##### How does the Integrals Calculator work?
Free Integrals Calculator - This lesson walks you through the integral definition, rules, and examples

### What 3 formulas are used for the Integrals Calculator?

limx → a ƒ(x) = L
ƒ(x) = c, then ∫ƒ(x) = cx + C
ƒ(x) = xn then ƒ'(x) = xn + 1/(n + 1)

For more math formulas, check out our Formula Dossier

### What 18 concepts are covered in the Integrals Calculator?

area
Number of square units covering the shape
constant
a value that always assumes the same value independent of how its parameters are varied
cos
cos(θ) is the ratio of the adjacent side of angle θ to the hypotenuse
cot
The length of the adjacent side divided by the length of the side opposite the angle. Also equals 1/tan(θ)
csc
the length of the hypotenuse divided by the length of the adjacent side. Also equals 1/sin(θ)
derivative
rate at which the value y of the function changes with respect to the change of the variable x
exponent
The power to raise a number
function
relation between a set of inputs and permissible outputs
ƒ(x)
graph
a pictorial representation or a diagram that represents data or values in an organized manner
integral
a mathematical object that can be interpreted as an area or a generalization of area
interval
a set of real numbers that contains all real numbers lying between any two numbers of the set
limit
the value that a function (or sequence) approaches as the input (or index) approaches some valu
logarithm
the exponent or power to which a base must be raised to yield a given number
power
how many times to use the number in a multiplication
sec
the length of the hypotenuse divided by the length of the adjacent side. Also equals 1/cos(θ)
sin
sin(θ) is the ratio of the opposite side of angle θ to the hypotenuse
tan
the ratio of the opposite side to the adjacent side of a particular angle of the right triangle.
variable
Alphabetic character representing a number