1. What is an Integral?

An integral is a fundamental concept in calculus that represents the area under a curve or the antiderivative of a function. It's the reverse operation of differentiation.

2. How Does the Calculator Work?

The calculator finds the antiderivative of the given function:

Where:

• \( f(x) \) — The function to integrate
• \( F(x) \) — The antiderivative of f(x)
• \( C \) — Constant of integration

Explanation: The calculator uses symbolic computation to find the function whose derivative matches the input function.

3. Importance of Integration

Details: Integration is essential for calculating areas, volumes, displacement, and many other quantities in physics, engineering, and economics.

4. Using the Calculator

Tips: Enter mathematical functions using standard notation (e.g., x^2 for x squared, sin(x) for sine function). The calculator supports basic functions and polynomials.

5. Frequently Asked Questions (FAQ)

Q1: What is the constant of integration?
A: Since derivatives of constants are zero, we add "+ C" to represent all possible antiderivatives.

Q2: Can this calculator do definite integrals?
A: This version calculates indefinite integrals only. For definite integrals, you would need to evaluate the antiderivative at the bounds.

Q3: What functions are supported?
A: Basic polynomials, trigonometric, exponential, and logarithmic functions.

Q4: Why doesn't my complex function work?
A: This calculator has limited pattern matching. For advanced functions, consider specialized math software.

Q5: How accurate are the results?
A: Results are mathematically exact for supported functions, as they use symbolic computation rather than numerical approximation.