Find Integration Calculator

What is Integration?

Integration is the reverse process of differentiation. While differentiation finds the rate of change of a function, integration finds the area under the curve of a function or the accumulation of quantities over an interval.

There are two main types of integration:

• Definite Integration: Calculates the exact area under a curve between two specified limits.
• Indefinite Integration: Finds the antiderivative of a function, which represents the family of curves that have the given function as their derivative.

Our calculator focuses on definite integration, which is widely used in physics, engineering, economics, and other fields to solve problems involving accumulation or area calculation.

How to Use This Calculator

Using our Find Integration Calculator is simple:

1. Enter the function you want to integrate in the "Function" field. For example, "x^2" or "sin(x)".
2. Specify the lower and upper limits of integration in the "Lower Limit" and "Upper Limit" fields.
3. Click the "Calculate" button to compute the definite integral.
4. View the result, which includes the computed integral value and a visual graph of the function.

The Integration Formula

The definite integral of a function f(x) from a to b is given by:

This formula approximates the area under the curve by summing the areas of rectangles under the curve. The more subintervals (n) you use, the more accurate the result.

Worked Examples

Example 1: Integrating x² from 0 to 1

Using our calculator:

1. Enter Function: x^2
2. Lower Limit: 0
3. Upper Limit: 1
4. Click Calculate

The result is approximately 0.3333, which matches the exact value of ∫[0 to 1] x² dx = 1/3.

Example 2: Integrating sin(x) from 0 to π

Using our calculator:

1. Enter Function: sin(x)
2. Lower Limit: 0
3. Upper Limit: π (use 3.14159)
4. Click Calculate

The result is approximately 2.0000, which matches the exact value of ∫[0 to π] sin(x) dx = 2.