Integral-Calculator.com

An integral calculator computes the area under a curve or the antiderivative of a function. This tool handles definite and indefinite integrals for polynomial, trigonometric, exponential, and logarithmic functions.

What is an Integral?

In calculus, an integral represents the area under a curve between two points. It can be computed as the limit of a Riemann sum. There are two main types of integrals:

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

Integrals have applications in physics, engineering, economics, and many other fields where accumulation of quantities is important.

Types of Integrals

Common integral types include:

Polynomial Integrals: Integrals of polynomials like x², x³, etc.
Trigonometric Integrals: Integrals of sine, cosine, tangent, etc.
Exponential Integrals: Integrals of eˣ, eˣⁿ, etc.
Logarithmic Integrals: Integrals involving natural logarithms.

This calculator supports all these types with precise computation.

How to Use This Calculator

To compute an integral:

Select the type of integral (definite or indefinite).
Enter the function you want to integrate.
For definite integrals, specify the lower and upper limits.
Click "Calculate" to get the result.

Note: The calculator uses standard mathematical notation. For example, enter "x^2" as x², "sin(x)" as sin(x), and "e^x" as e^x.

Examples

Here are some example calculations:

Function	Type	Result
x²	Indefinite	(1/3)x³ + C
sin(x)	Indefinite	-cos(x) + C
x²	Definite (0 to 1)	1/3
e^x	Definite (0 to 1)	e - 1

FAQ

What is the difference between definite and indefinite integrals?

A definite integral computes the exact area under a curve between two limits, while an indefinite integral finds the antiderivative of a function, which represents the family of curves that have the given function as their derivative.

What types of functions can this calculator handle?

This calculator supports polynomial, trigonometric, exponential, and logarithmic functions. It can compute both definite and indefinite integrals for these function types.

How accurate are the calculations?

The calculator uses precise mathematical algorithms to compute integrals. For most common functions, the results are exact. For more complex functions, the calculator provides an approximate result.