Integral. Calculator

An integral calculator helps you compute definite and indefinite integrals quickly. Whether you're a student studying calculus or a professional working with mathematical models, this tool provides accurate results and visual representations of your calculations.

What is an Integral?

In calculus, an integral represents the area under a curve or the accumulation of quantities. Integrals are used to find areas, volumes, central points, and many other important mathematical concepts. There are two main types of integrals: definite and indefinite.

Definite integrals calculate the exact area under a curve between two points, while indefinite integrals find the antiderivative of a function, which represents the family of curves that could produce the original function when differentiated.

Types of Integrals

Definite Integral

A definite integral calculates the exact area under a curve between two specified limits, denoted as a and b. The formula for a definite integral is:

∫[a to b] f(x) dx = F(b) - F(a)

Where F(x) is the antiderivative of f(x).

Indefinite Integral

An indefinite integral finds the antiderivative of a function, which represents the family of curves that could produce the original function when differentiated. The result includes a constant of integration, denoted as C.

∫ f(x) dx = F(x) + C

How to Use This Calculator

Select the type of integral you want to calculate (definite or indefinite).
Enter the function you want to integrate. For example, "x^2" or "sin(x)".
If calculating a definite integral, enter the lower and upper limits.
Click "Calculate" to see the result and a visual representation of the integral.

This calculator supports basic mathematical functions and operations. For complex integrals, you may need to use more advanced tools or software.

Formula Used

The calculator uses numerical integration methods to approximate definite integrals. For indefinite integrals, it finds the antiderivative using symbolic computation.

Definite Integral: ∫[a to b] f(x) dx ≈ Σ f(x_i) Δx Indefinite Integral: ∫ f(x) dx = F(x) + C

Examples

Example 1: Definite Integral

Calculate the integral of x^2 from 0 to 1.

Result: 0.3333 (approximately 1/3)

Example 2: Indefinite Integral

Find the antiderivative of x^2.

Result: (1/3)x^3 + C

FAQ

What is the difference between definite and indefinite integrals?

A definite integral calculates the exact area under a curve between two points, while an indefinite integral finds the antiderivative of a function, which represents the family of curves that could produce the original function when differentiated.

Can this calculator handle complex functions?

This calculator supports basic mathematical functions and operations. For complex integrals, you may need to use more advanced tools or software.

How accurate are the results?

The calculator uses numerical integration methods for definite integrals and symbolic computation for indefinite integrals. Results are accurate for most common mathematical functions.