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ƒ()
ƒ'()

n =

Given ƒ(x) = 5x3dx
Determine the integral ∫ƒ(x)
Go through and integrate each term

itarget = 0,1

Integrate term 1

ƒ(x) = 5x3

Use the power rule

∫ƒ(x) of the expression axn
ax(n + 1)
n + 1

= 5, n = 3
and x is the variable we integrate
∫ƒ(x)  =  5x(3 + 1)
  3 + 1

∫ƒ(x)  =  5x4
  4


Collecting all of our integrated terms we get:

∫ƒ(x) = 5x4/4

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) 1st Derivative ƒ‘(x)  The derivative of your expression will also be evaluated at a point, i.e., ƒ‘(1)
3) 2nd 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) = xn, 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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