# Functions-Derivatives-Integrals Calculator

Given ƒ(x) = 5x

^{3}dx

Determine the integral ∫ƒ(x)

Go through and integrate each term

## Integrate term 1

ƒ(x) = 5x

^{3}## Use the power rule

∫ƒ(x) of the expression ax

^{n} = 5, n = 3

and x is the variable we integrate

∫ƒ(x) = | 5x^{(3 + 1)} |

| 3 + 1 |

## Collecting all of our integrated terms we get:

∫ƒ(x) =

**5x**^{4}/4## Evaluate ∫ƒ(x) on the interval [0,1]

The value of the integral over an interval is ∫ƒ(1) - ∫ƒ(0)

## Evaluate ∫ƒ(1)

∫ƒ(1) = 5(

1)

^{4}/4

∫ƒ(1) = 5(1)/4

∫ƒ(1) = 1.25

∫ƒ(1) =

**1.25**## Evaluate ∫ƒ(0)

∫ƒ(0) = 5(

0)

^{4}/4

∫ƒ(0) = 5(0)/4

∫ƒ(0) = 0

∫ƒ(0) =

**0**## Determine our answer

∫ƒ(x) on the interval [0,1] = ∫ƒ(1) - ∫ƒ(0)

∫ƒ(x) on the interval [0,1] = 1.25 - 0

##### Final Answer

∫ƒ(x) on the interval [0,1] = **1.25**

##### What is the Answer?

∫ƒ(x) on the interval [0,1] = **1.25**

##### How does the Functions-Derivatives-Integrals Calculator work?

Free Functions-Derivatives-Integrals Calculator - Given a polynomial expression, this calculator evaluates the following items:

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1^{st} Derivative ƒ‘(x) The derivative of your expression will also be evaluated at a point, i.e., ƒ‘(1)

3) 2^{nd} Derivative ƒ‘‘(x) The second derivative of your expression will be also evaluated at a point, i.e., ƒ‘‘(1)

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

This calculator has 7 inputs.

### What 1 formula is used for the Functions-Derivatives-Integrals Calculator?

Power Rule:
f(x) = x

^{n}, f‘(x) = nx

^{(n - 1)}For more math formulas, check out our

Formula Dossier
### What 8 concepts are covered in the Functions-Derivatives-Integrals Calculator?

- 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) - functions-derivatives-integrals
- integral
- a mathematical object that can be interpreted as an area or a generalization of area
- point
- an exact location in the space, and has no length, width, or thickness
- polynomial
- an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
- power
- how many times to use the number in a multiplication

##### Example calculations for the Functions-Derivatives-Integrals Calculator

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