1. What is a Definite Integral?

A definite integral represents the signed area under a curve between two points on the x-axis. It's a fundamental concept in calculus with applications in physics, engineering, and many other fields.

2. How Does the Integral Calculator Work?

The calculator computes the definite integral using numerical methods:

Where:

• \( f(x) \) — The function to integrate
• \( a \) — Lower limit of integration
• \( b \) — Upper limit of integration

Explanation: The calculator uses numerical approximation techniques to estimate the area under the curve between the specified limits.

3. Importance of Integral Calculation

Details: Integral calculations are essential for determining areas, volumes, work done, center of mass, and many other physical quantities in mathematics and science.

4. Using the Calculator

Tips: Enter a valid mathematical function f(x), and specify the lower and upper limits of integration. The calculator will approximate the definite integral.

5. Frequently Asked Questions (FAQ)

Q1: What types of functions can I integrate?
A: The calculator can handle polynomial, trigonometric, exponential, and logarithmic functions, among others.

Q2: How accurate are the results?
A: The accuracy depends on the numerical method used but typically provides results precise to several decimal places.

Q3: Can I use variables other than x?
A: The calculator currently only supports functions of x as the variable of integration.

Q4: What if my function has discontinuities?
A: The calculator may not handle discontinuous functions properly. For such functions, consider breaking the integral into parts.

Q5: Can I calculate indefinite integrals?
A: This calculator is designed for definite integrals only. For indefinite integrals, you would need a symbolic calculator.