1. What is Area Under Curve?

The area under a curve represents the integral of a function between two points. It has applications in physics, engineering, probability, and many other fields where accumulated quantities need to be measured.

2. How Does the Calculator Work?

The calculator uses numerical integration to approximate:

Where:

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

Explanation: The calculator numerically approximates the integral using methods like Simpson's rule or the trapezoidal rule.

3. Importance of Area Calculation

Details: Calculating area under curves is fundamental in determining work done in physics, probabilities in statistics, accumulated growth in biology, and many other applications.

4. Using the Calculator

Tips: Enter a valid mathematical function (like "sin(x)", "x^2+3", etc.), and the upper and lower limits. The calculator will approximate the area under the curve between these limits.

5. Frequently Asked Questions (FAQ)

Q1: What functions can I enter?
A: The calculator supports basic mathematical functions like polynomials, trigonometric, exponential, and logarithmic functions.

Q2: How accurate is the calculation?
A: The accuracy depends on the numerical method used and the step size. More complex functions may require more precise methods.

Q3: Can I calculate improper integrals?
A: This calculator is designed for definite integrals with finite limits. For improper integrals, specialized methods are needed.

Q4: What if my function has discontinuities?
A: The calculator may give inaccurate results for discontinuous functions. The integral may not exist in some cases.

Q5: Can I use variables other than x?
A: Currently, the calculator only supports functions of x as the variable of integration.