1. What is Calculus?

Calculus is a branch of mathematics that studies continuous change. It has two major branches: differential calculus (concerning rates of change and slopes of curves) and integral calculus (concerning accumulation of quantities and areas under curves).

2. How Does the Calculator Work?

The calculator performs basic calculus operations:

Where:

• \( f(x) \) — Mathematical function of variable x
• \( \int \) — Integral symbol representing accumulation
• \( \frac{d}{dx} \) — Derivative operator representing rate of change

Explanation: The calculator uses symbolic computation to find exact solutions to differentiation and integration problems.

3. Importance of Calculus

Details: Calculus is fundamental to physics, engineering, economics, statistics, and many other fields. It's used to model and solve problems involving change and motion.

4. Using the Calculator

Tips: Enter a valid mathematical function using standard notation (e.g., "x^2 + sin(x)"). Select the operation (integral or derivative) and specify the variable of integration/differentiation.

5. Frequently Asked Questions (FAQ)

Q1: What functions can the calculator handle?
A: The calculator can handle polynomials, trigonometric, exponential, and logarithmic functions.

Q2: Does the calculator show steps?
A: This basic version shows only the final result. Advanced versions may show step-by-step solutions.

Q3: How accurate are the results?
A: The calculator provides exact symbolic solutions, not numerical approximations.

Q4: Can I calculate definite integrals?
A: This version calculates indefinite integrals. For definite integrals, you would need to specify limits of integration.

Q5: What about partial derivatives or multiple integrals?
A: This calculator handles single-variable calculus only. For multivariable calculus, you would need an advanced version.