Calculate Your Integral
Integration Result
Your result will appear here
Step-by-Step Solution
Step-by-step solution will be shown here
Integral Calculator - Solve Definite and Indefinite Integrals
Our free online integral calculator allows you to find definite and indefinite integrals step-by-step. Perfect for students, engineers, and mathematicians.
What is Integral Calculus?
Integral calculus is a fundamental branch of mathematics focused on integrals and their properties. It's used to calculate areas, volumes, displacement, and other concepts that arise from combining infinitesimal data. Integration is the inverse process of differentiation, making these two concepts central to calculus.
Types of Integrals
Our integral calculator can handle both types of integrals:
- Indefinite Integrals: Represent antiderivatives and include a constant of integration (C)
- Definite Integrals: Calculate the net area between the function graph and the x-axis over a specific interval
Applications of Integration
Integration has numerous practical applications in various fields:
- Physics: Calculating center of mass, work done, and moment of inertia
- Engineering: Determining structural loads and fluid dynamics
- Economics: Modeling consumer and producer surplus
- Probability: Defining continuous probability distributions
Frequently Asked Questions
How does this integral calculator work?
Our calculator uses mathematical algorithms to symbolically compute integrals. It applies standard integration rules including power rule, substitution, integration by parts, and partial fractions to solve your integration problems.
Can I calculate definite integrals with this tool?
Yes, simply enter the lower and upper limits to compute definite integrals. Leave these fields blank for indefinite integrals.
What functions are supported by this calculator?
Our calculator supports polynomial, rational, exponential, logarithmic, trigonometric, and hyperbolic functions, among others.
Does the calculator show step-by-step solutions?
Yes, after calculating an integral, you can see the step-by-step process to understand how the solution was derived.
Is this integral calculator free to use?
Absolutely! Our integral calculator is completely free with no registration required.
