A numerical value:

Area under the graph of a

function for some interval.

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

lim_{x → a}ƒ(x) = L

∫ƒ(x) dx.integral of f of x dx.

ƒ(x) = 6, then ∫ƒ(x) = 6x + CIntegral of a constant n is

nx + C.

ƒ(x) = x^{n}, then ∫ƒ(x)dx is:

x^{n + 1} | |

n + 1 |

Using the power rule with n = 2

∫ƒ(x) = x

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 |

ƒ(x) | ƒ'(x) |
---|---|

e^{x} | e^{x} |

a^{x} | a^{x}/Ln(a) where a > 0, a ≠ 1 |

Ln(x) | 1/x |

log_{a}x | x * Ln(x) - x |

Free Integrals Calculator - This lesson walks you through the integral definition, rules, and examples

lim_{x → a} ƒ(x) = L

ƒ(x) = c, then ∫ƒ(x) = cx + C

ƒ(x) = x^{n} then ƒ'(x) = x^{n + 1}/(n + 1)

For more math formulas, check out our Formula Dossier

ƒ(x) = c, then ∫ƒ(x) = cx + C

ƒ(x) = x

For more math formulas, check out our Formula Dossier

- 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

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