Simple Integral Calculator

What is an Integral?

An integral represents the area under a curve between two points. It's a fundamental concept in calculus that has applications in physics, engineering, economics, and many other fields. There are two main types of integrals:

• Definite Integral: Calculates the exact area under a curve between specified limits.
• Indefinite Integral: Finds the antiderivative of a function, which represents the family of functions whose derivative is the original function.

Integrals are calculated using various techniques, including substitution, integration by parts, and partial fractions. This calculator focuses on basic functions that can be integrated using elementary methods.

How to Use This Calculator

1. Select whether you want to calculate a definite or indefinite integral.
2. Enter the function you want to integrate in the function field.
3. For definite integrals, enter the lower and upper limits.
4. Click "Calculate" to get the result.
5. Review the solution and chart (if available) for better understanding.

Formula Explained

The calculator uses these formulas to compute the integrals of basic functions. For more complex functions, additional techniques like substitution or integration by parts may be required.

Worked Examples

Example 1: Definite Integral

Calculate the integral of x² from 0 to 1.

Solution:

1. Find the antiderivative of x²: (1/3)x³
2. Evaluate at the upper limit (1): (1/3)(1)³ = 1/3
3. Evaluate at the lower limit (0): (1/3)(0)³ = 0
4. Subtract: 1/3 - 0 = 1/3

The result is 1/3.

Example 2: Indefinite Integral

Find the integral of sin(x).

Solution:

1. The antiderivative of sin(x) is -cos(x) + C

The result is -cos(x) + C.