Free Integral Calculator with Steps

Integrals are fundamental in calculus and have applications in physics, engineering, and economics. This calculator helps you compute integrals with detailed step-by-step solutions.

What is an Integral?

An integral represents the area under a curve or the accumulation of quantities. In calculus, integrals are used to find areas, volumes, and to solve differential equations.

The integral of a function f(x) with respect to x is written as ∫f(x)dx. The result is called the antiderivative of f(x).

Basic Integral Formula:

∫f(x)dx = F(x) + C, where F'(x) = f(x) and C is the constant of integration.

Integrals can be computed using various techniques including substitution, integration by parts, and partial fractions.

Types of Integrals

There are two main types of integrals:

1. Definite Integral

A definite integral has limits of integration and represents the area under the curve between two points.

∫[a to b] f(x)dx = F(b) - F(a)

2. Indefinite Integral

An indefinite integral does not have limits and represents a family of functions.

∫f(x)dx = F(x) + C

Both types are supported by this calculator.

How to Use This Calculator

Enter the function you want to integrate in the input field. Select whether you want a definite or indefinite integral. For definite integrals, enter the lower and upper limits.

The calculator will display the result with step-by-step solutions.

Tip: Use standard mathematical notation. For example, enter "x^2 + 3x" for the function x² + 3x.

Common Integral Examples

Here are some common integrals and their solutions:

Example 1: ∫x² dx

Solution: (1/3)x³ + C

Example 2: ∫[1 to 2] x dx

Solution: (2²)/2 - (1²)/2 = 2 - 0.5 = 1.5

Example 3: ∫sin(x) dx

Solution: -cos(x) + C

FAQ

What is the difference between definite and indefinite integrals?: A definite integral has limits of integration and gives a numerical value, while an indefinite integral represents a family of functions.
Can this calculator handle complex functions?: Yes, the calculator can handle a wide range of functions, including polynomials, trigonometric, exponential, and logarithmic functions.
How accurate are the step-by-step solutions?: The solutions are generated using standard calculus techniques and are accurate for the given functions.
Is this calculator free to use?: Yes, this calculator is completely free to use with no restrictions.
Can I use this calculator on my mobile device?: Yes, the calculator is fully responsive and works on all devices, including mobile phones and tablets.