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

**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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