Given ƒ(x) = 12x
3dx
Determine the integral ∫ƒ(x)
Go through and integrate each term
itarget = 1,2
Integrate term 1
ƒ(x) = 12x
3Use the power rule
∫ƒ(x) of the expression ax
n = 12, n = 3
and x is the variable we integrate
Simplify our fraction.
Divide top and bottom by 4
∫ƒ(x) = 3x
4
Collecting all of our integrated terms we get:
∫ƒ(x) =
3x4Evaluate ∫ƒ(x) on the interval [1,2]
The value of the integral over an interval is ∫ƒ(2) - ∫ƒ(1)
Evaluate ∫ƒ(2)
∫ƒ(2) = 3(
2)
4∫ƒ(2) = 3(16)
∫ƒ(2) = 48
∫ƒ(2) =
48Evaluate ∫ƒ(1)
∫ƒ(1) = 3(
1)
4∫ƒ(1) = 3(1)
∫ƒ(1) = 3
∫ƒ(1) =
3Determine our answer
∫ƒ(x) on the interval [1,2] = ∫ƒ(2) - ∫ƒ(1)
∫ƒ(x) on the interval [1,2] = 48 - 3
Final Answer
∫ƒ(x) on the interval [1,2] = 45
You have 2 free calculationss remaining
What is the Answer?
∫ƒ(x) on the interval [1,2] = 45
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) = 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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