1. What is Integration?

Integration is a fundamental concept in calculus that represents the accumulation of quantities and the area under curves. The integral of a function f(x) with respect to x is denoted as ∫f(x)dx.

2. How Does the Calculator Work?

The calculator processes mathematical functions to find their integrals:

Where:

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

Explanation: The integral calculates the area under the curve of the function between specified limits (for definite integrals) or finds the antiderivative (for indefinite integrals).

3. Importance of Integration

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

4. Using the Calculator

Tips: Enter a valid mathematical function using standard notation (e.g., x^2 for x squared, sin(x) for sine of x). For definite integrals, specify both lower and upper limits.

5. Frequently Asked Questions (FAQ)

Q1: What functions can I integrate with this calculator?
A: The calculator supports polynomials, trigonometric, exponential, and logarithmic functions.

Q2: How accurate are the results?
A: For symbolic integration, results are exact. For numerical integration, accuracy depends on the method used.

Q3: Can I integrate multivariate functions?
A: Currently, the calculator supports single-variable integration only.

Q4: What's the difference between definite and indefinite integrals?
A: Definite integrals compute a numerical value (area under curve between limits), while indefinite integrals find the antiderivative function.

Q5: Can I see step-by-step solutions?
A: Advanced versions may show step-by-step solutions, but this basic version provides final results only.