The area under the curve calculator is a free online tool to find the area of a curve. Protonstalk area under the curve calculator is one such handy tool to display the area under the curve within specified limits.
About Area Under the Curve Calculator
Inputs
The inputs of the calculator are:
- Function of the curve
- Lower limit (to get a definite area)
- Upper limit (to get a definite area)
Steps to Use
Step 1: Enter the function, upper limit as well lower limit in input fields.
Step 2: Click “Calculate Area” to compute the area under the curve.
Step 3: The result displays in a new window.
Outputs
The outputs of the calculator are:
- Area under the curve
- Graphical representation of the required area.
Area under a curve
In mathematics, The area under a curve is a definite integral of that curve between two points. For the function f(x), the area of the resulting curve between limits x=a and x=b. The area above the x-axis is the positive area and the area under the x-axis is the negative area.
General Form : A = \(\int_{a}^{b}f(x)dx\)
Related: Definite Integral Properties
Example
Find the area under the curve f(x) = \(x^{2}\) between limits x = 2 and x =4.
We know the general form to be A = \(\int_{a}^{b}f(x)dx\)
here f(x) = \(x^{2}\), a = 2 and b = 4
So, we get \(\int_{2}^{4}x^{2}dx\)
Solving the integral we get, \([\frac{x^3}{3}]_{2}^{4}\)
This gives us \(\frac{64}{3} – \frac{8}{3}\)
Apply the limits we get 56/3
=> 18.667
Therefore, the area under the curve \(x^{2}\) between the given limits is 18.667
FAQs
The area under a curve obviously between two points is found out by doing a definite integral of theat function between the two points.
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