Maths Integral Calculator
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Reviewed by Calculator Editorial Team
This maths integral calculator helps you compute definite and indefinite integrals quickly. Whether you're a student studying calculus or a professional needing quick calculations, this tool provides accurate results with step-by-step explanations.
What is an Integral?
In calculus, an integral represents the area under a curve between two points. It's the reverse process of differentiation. Integrals have many applications in physics, engineering, economics, and more.
There are two main types of integrals: definite and indefinite.
Indefinite Integral Formula
∫f(x) dx = F(x) + C
Where F(x) is the antiderivative of f(x) and C is the constant of integration.
Definite Integral Formula
∫[a to b] f(x) dx = F(b) - F(a)
Where F(x) is the antiderivative of f(x), evaluated from a to b.
Types of Integrals
Indefinite Integrals
Indefinite integrals find the antiderivative of a function. They represent a family of functions that differ by a constant.
Definite Integrals
Definite integrals calculate the exact area under a curve between two specified limits. They provide a single numerical value.
Improper Integrals
Improper integrals extend to infinity or have points of discontinuity within the interval of integration.
Multiple Integrals
Multiple integrals extend the concept of integration to functions of several variables.
How to Use This Calculator
- Select the type of integral you want to calculate (definite or indefinite).
- Enter the function you want to integrate in the function field.
- For definite integrals, enter the lower and upper limits.
- Click "Calculate" to get the result.
- Review the result and explanation provided.
Note: This calculator supports basic mathematical functions. For complex integrals, you may need more advanced software.
Examples
Example 1: Indefinite Integral
Calculate ∫x² dx
Result: (1/3)x³ + C
Example 2: Definite Integral
Calculate ∫[0 to 1] x² dx
Result: 1/3
| Function | Indefinite Integral | Definite Integral (0 to 1) |
|---|---|---|
| x | (1/2)x² + C | 1/2 |
| x² | (1/3)x³ + C | 1/3 |
| sin(x) | -cos(x) + C | 2 |
FAQ
What is the difference between definite and indefinite integrals?
Definite integrals provide a single numerical value representing the area under a curve between two points, while indefinite integrals find the antiderivative of a function, representing a family of functions that differ by a constant.
Can this calculator handle complex functions?
This calculator supports basic mathematical functions. For complex integrals, you may need more advanced software or mathematical knowledge.
What if I get an error when calculating an integral?
Errors can occur if the function is not properly formatted or if the integral cannot be computed. Double-check your input and try again.
Is this calculator free to use?
Yes, this calculator is completely free to use with no restrictions.