1. What is Net Change?

The net change represents the accumulated change in a quantity over an interval. Mathematically, it's calculated as the definite integral of a rate of change function over a specified interval.

2. How Does the Calculator Work?

The calculator uses the fundamental theorem of calculus:

Where:

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

Explanation: The integral sums up all the infinitesimal changes over the interval [a, b] to give the total net change.

3. Importance of Net Change Calculation

Details: Net change calculations are fundamental in physics (displacement from velocity), economics (total profit from marginal profit), and many other fields where accumulation of change is important.

4. Using the Calculator

Tips: Enter a valid mathematical function, and the lower and upper limits of integration. The function should be continuous over the interval [a, b].

5. Frequently Asked Questions (FAQ)

Q1: What types of functions can I enter?
A: The calculator should support polynomial, trigonometric, exponential, and logarithmic functions.

Q2: What if my function has discontinuities?
A: The integral may not exist or may need to be calculated as an improper integral in such cases.

Q3: How accurate are the results?
A: Accuracy depends on the numerical integration method used. Most calculators provide results accurate to several decimal places.

Q4: Can I use variables other than x?
A: Typically, the variable of integration is x, but some calculators might allow other variables.

Q5: What if my limits are reversed (a > b)?
A: The result will simply be the negative of the integral from b to a.