1. What is a Definite Integral?

The definite integral of a function between two limits represents the signed area under the curve of that function between those two points. It's a fundamental concept in calculus with applications in physics, engineering, and probability.

2. How Does the Calculator Work?

The calculator uses the Fundamental Theorem of Calculus:

Where:

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

Explanation: The integral calculates the net area between the function curve and the x-axis from point a to point b.

3. Importance of Integral Calculation

Details: Definite integrals are essential for calculating areas, volumes, displacement, work, and many other physical quantities in science and engineering applications.

4. Using the Calculator

Tips: Enter a valid mathematical function (like "x^2 + 3*x - 5"), the lower and upper limits. The calculator will compute the definite integral between these limits.

5. Frequently Asked Questions (FAQ)

Q1: What functions can I integrate with this calculator?
A: The calculator can handle polynomial, trigonometric, exponential, and logarithmic functions (implementation dependent).

Q2: What if my integral doesn't converge?
A: The calculator will indicate if the integral is divergent or if the function is undefined in the interval.

Q3: Can I use variables other than x?
A: Currently, the calculator only accepts 'x' as the variable of integration.

Q4: How precise are the results?
A: Results are typically precise to 8 decimal places, depending on the implementation.

Q5: Can I calculate improper integrals?
A: Yes, if the calculator supports infinite limits or singularities within the interval.