Applications of Integrals · Centroids & Averages
Net Change Theorem
The integral of a rate of change gives the net change. This is just FTC Part 2 interpreted in context.
- 0 variables
- 2 worked examples
- 14 in Applications of Integrals
Worked examples
A population grows at rate P'(t) = 100e^(0.02t). Find the population increase from t = 0 to t = 10.
- ∫₀¹⁰ 100e^(0.02t) dt = 100[e^(0.02t)/0.02]₀¹⁰ = 5000(e^0.2 - 1)
Answer: 5000(e^0.2 - 1) ≈ 1107 individuals
1 more worked examplePremium
Water flows into a tank at r(t) = 6t litres per minute. How much water enters between t = 2 and t = 5 minutes?
Step-by-step solution locked.
Unlock the full working. CalcRef Premium opens the step-by-step solution above, and 141 worked solutions across the whole library - the intermediate lines, not just the answer. The formula statement, its conditions, its variables and the first worked example stay free on every page.
See all 14 Applications of Integrals formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.
Practice
Quiz yourself on Applications of Integrals
Net Change Theorem is one of 14 Applications of Integrals formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.