Online Integral Calculator with Limits
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Reviewed by Calculator Editorial Team
An online integral calculator with limits helps solve definite and indefinite integrals in calculus. This tool computes the area under a curve or the antiderivative of a function, providing both numerical results and visual graphs.
What is an Integral Calculator?
An integral calculator is a digital tool that computes integrals, which are fundamental in calculus. Integrals can be definite (with limits) or indefinite (without limits).
Definite integrals calculate the area under a curve between two points, while indefinite integrals find the antiderivative of a function. This calculator provides both types of solutions with clear explanations.
How to Use This Calculator
- Enter the function you want to integrate in the "Function" field.
- For definite integrals, enter the lower and upper limits in the respective fields.
- Click "Calculate" to compute the integral.
- Review the result, which includes the integral value and a visual graph.
Use standard mathematical notation. For example, enter "x^2" as x^2, "sin(x)" as sin(x), and "e^x" as e^x.
Formula Used
For definite integrals:
∫[a to b] f(x) dx = F(b) - F(a)
Where F(x) is the antiderivative of f(x).
For indefinite integrals:
∫ f(x) dx = F(x) + C
Where C is the constant of integration.
Worked Example
Let's compute the definite integral of x^2 from 0 to 1.
- Enter the function: x^2
- Enter lower limit: 0
- Enter upper limit: 1
- Click "Calculate"
The calculator computes the antiderivative of x^2, which is (x^3)/3, and evaluates it from 0 to 1:
(1^3)/3 - (0^3)/3 = 1/3 - 0 = 1/3 ≈ 0.3333
The result is 0.3333, which represents the area under the curve x^2 from 0 to 1.
Frequently Asked Questions
What is the difference between definite and indefinite integrals?
Definite integrals calculate the area under a curve between two points, while indefinite integrals find the antiderivative of a function.
How do I enter functions in the calculator?
Use standard mathematical notation. For example, enter "x^2" as x^2, "sin(x)" as sin(x), and "e^x" as e^x.
What if the calculator doesn't recognize my function?
Ensure you're using correct mathematical notation. The calculator supports basic functions, exponents, and trigonometric functions.