# Area Under the Curve Calculator

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:

1. Function of the curve
2. Lower limit (to get a definite area)
3. 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:

1. Area under the curve
2. 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 = $$\int_{a}^{b}f(x)dx$$

## 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

How do you find area under a curve?

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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