1. What is an Integral?

An integral is a fundamental concept in calculus that represents the area under a curve or the accumulation of quantities. The indefinite integral ∫f(x)dx represents the antiderivative of f(x).

2. How Does the Calculator Work?

The calculator computes the antiderivative of the given function:

Where:

• \( f(x) \) — The function to integrate
• \( dx \) — The variable of integration

Explanation: The integral finds the function F(x) whose derivative is f(x), plus an arbitrary constant C.

3. Importance of Integration

Details: Integration is essential in mathematics, physics, engineering, and many other fields for solving problems involving areas, volumes, displacement, and accumulation.

4. Using the Calculator

Tips: Enter a valid mathematical function of x. Supported operations typically include basic arithmetic, trigonometric, exponential, and logarithmic functions.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between definite and indefinite integrals?
A: Indefinite integrals give a general antiderivative (plus C), while definite integrals compute a numerical value over an interval [a,b].

Q2: What does the +C mean in integration?
A: The +C represents the constant of integration, since the derivative of any constant is zero.

Q3: Can all functions be integrated analytically?
A: No, some functions don't have elementary antiderivatives and require numerical methods.

Q4: What are common integration techniques?
A: Substitution, integration by parts, partial fractions, and trigonometric substitution are common methods.

Q5: How accurate is this calculator?
A: The accuracy depends on the implementation. Symbolic integration provides exact results when possible.