Integral Calculator

Compute definite and indefinite integrals with detailed step-by-step solutions!

Integral Calculator

Compute the Integral:

Try the following examples:

[Polynomial Integration] [Trigonometric Integration] [Exponential Integration] [Rational Function Integration] [Linear Function Integration] [Logarithmic Integration] [Inverse Trigonometric Integration] [Hyperbolic Function Integration]

Function to Integrate:
Variable of Integration:
Lower Limit (optional):	Leave blank to compute the indefinite integral.
Upper Limit (optional):	Leave blank to compute the indefinite integral.

Embed Integral Calculator Widget

About Integral Calculator

Welcome to our Integral Calculator, a powerful tool designed to compute definite and indefinite integrals with detailed step-by-step solutions and visualizations. This calculator is ideal for students, teachers, and anyone working with calculus and integration.

Features of the Integral Calculator

Step-by-Step Solutions: Understand each step involved in computing integrals.
Area Visualization: Graphically represent the area under the curve for definite integrals.
Comprehensive Results: View both indefinite and definite integrals.
User-Friendly Interface: Input functions easily and get instant results.
Accurate Computations: Utilizes symbolic computation for precise results.

Understanding Integration

Integration is a fundamental concept in calculus that represents the accumulation of quantities and the area under a curve.

Indefinite Integral

The indefinite integral of a function \( f(x) \) is the set of all antiderivatives of \( f(x) \), represented as:

\[ \int f(x) \, dx = F(x) + C \]

Where:

\( F(x) \) is the antiderivative of \( f(x) \)
\( C \) is the constant of integration

Definite Integral

The definite integral of a function \( f(x) \) from \( a \) to \( b \) is given by:

\[ \int_{a}^{b} f(x) \, dx = F(b) - F(a) \]

It represents the net area under the curve \( f(x) \) from \( x = a \) to \( x = b \).

How to Use the Integral Calculator

Enter the function to integrate.
Enter the variable of integration (e.g., \( x \)).
Optionally, enter the lower limit and upper limit for definite integrals.
Click on "Compute Integral" to process your inputs.
View the integral result along with step-by-step solutions and graphs.

Applications of the Integral Calculator

Our integral calculator is especially useful for:

Calculus Students and Teachers: Learning and teaching integration techniques.
Engineers and Scientists: Solving real-world problems involving integration.
Anyone Interested in Mathematics: Understanding the concept of accumulation and area under curves.

Why Use Our Integral Calculator?

Calculating integrals manually can be complex and time-consuming. Our calculator simplifies the process by providing:

Accuracy: Ensuring precise calculations using symbolic computation.
Efficiency: Saving time on homework, tests, or professional projects.
Educational Value: Enhancing understanding through detailed steps and visual aids.