1. What is an Integral?

The integral of a function represents the area under its curve and is the reverse operation of differentiation. The indefinite integral (antiderivative) is expressed as ∫f(x)dx = F(x) + C, where F(x) is the antiderivative and C is the constant of integration.

2. How Does the Calculator Work?

The calculator uses symbolic computation to find antiderivatives:

Where:

• \( f(x) \) — The integrand function (unit varies)
• \( F(x) \) — The antiderivative (unit varies)
• \( C \) — Constant of integration (unit varies)
• \( dx \) — Indicates integration with respect to x

Explanation: The calculator applies integration rules (power rule, substitution, parts, etc.) to find the most general antiderivative.

3. Importance of Integration

Details: Integration is fundamental in mathematics and physics for calculating areas, volumes, displacement, work, and many other quantities that accumulate over an interval.

4. Using the Calculator

Tips: Enter the function using standard mathematical notation (e.g., x^2 for x², sin(x) for sine function). Specify the variable of integration (default is x).

5. Frequently Asked Questions (FAQ)

Q1: What functions can be integrated?
A: The calculator can handle polynomials, trigonometric, exponential, logarithmic functions, and their combinations.

Q2: What does the +C mean?
A: It represents the constant of integration, since antiderivatives are only unique up to an additive constant.

Q3: Can definite integrals be calculated?
A: This calculator focuses on indefinite integrals. For definite integrals, evaluate the antiderivative at the bounds.

Q4: What if my function isn't integrable in elementary terms?
A: Some functions (e.g., e^(-x²)) have no elementary antiderivative and require numerical methods or special functions.

Q5: How accurate are the results?
A: Symbolic integration provides exact results when possible, unlike numerical methods which approximate.