Essential Concepts
- The net change theorem states that when a quantity changes, the final value equals the initial value plus the integral of the rate of change. Net change can be a positive number, a negative number, or zero.
- The area under an even function over a symmetric interval can be calculated by doubling the area over the positive [latex]x[/latex]-axis. For an odd function, the integral over a symmetric interval equals zero, because half the area is negative.
Key Equations
- Net Change Theorem
[latex]F(b)=F(a)+{\int }_{a}^{b}F\text{'}(x)dx[/latex] or [latex]{\displaystyle\int }_{a}^{b}F\text{'}(x)dx=F(b)-F(a)[/latex]
Glossary
- net change theorem
- if we know the rate of change of a quantity, the net change theorem says the future quantity is equal to the initial quantity plus the integral of the rate of change of the quantity
Candela Citations
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- Calculus Volume 1. Authored by: Gilbert Strang, Edwin (Jed) Herman. Provided by: OpenStax. Located at: https://openstax.org/details/books/calculus-volume-1. License: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike. License Terms: Access for free at https://openstax.org/books/calculus-volume-1/pages/1-introduction