1. What is an Integral Calculator?

An integral calculator computes the antiderivative (indefinite integral) or the area under a curve (definite integral) of a given mathematical function. It's a powerful tool for solving calculus problems.

2. How Does the Calculator Work?

The calculator uses symbolic computation to find integrals:

Where:

• \( f(x) \) — The function to integrate
• \( a, b \) — Lower and upper limits (for definite integrals)
• \( dx \) — Indicates integration with respect to x

3. Types of Integrals

Indefinite Integrals: Find the general antiderivative plus constant of integration.

Definite Integrals: Compute the exact area under the curve between two points.

4. Using the Calculator

Tips: Enter the function using standard mathematical notation. For definite integrals, specify both limits. Common functions include sin(x), cos(x), exp(x), ln(x), etc.

5. Frequently Asked Questions (FAQ)

Q1: What functions can this calculator handle?
A: It can handle polynomials, trigonometric, exponential, logarithmic functions, and their combinations.

Q2: How are definite integrals different from indefinite?
A: Definite integrals compute a numerical value (area), while indefinite integrals find a family of functions (antiderivatives).

Q3: What does the +C mean in results?
A: For indefinite integrals, +C represents the constant of integration since antiderivatives are only unique up to a constant.

Q4: Can it handle improper integrals?
A: Yes, it can evaluate integrals with infinite limits or singularities.

Q5: What integration techniques does it use?
A: It uses substitution, integration by parts, partial fractions, and other advanced techniques.