Interpreting Definite Integrals

Grade 11•45 minutes•AP Central 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integration AP Central 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts

Learning Objective

I can apply definite integrals to solve problems involving displacement, total distance, and accumulation of quantities.

Practice Questions

This lesson includes 7 practice questions to reinforce learning.

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1. Explain in your own words what the definite integral of a rate function represents in a real-world context. Give an example.

2. A water tank is being filled at a rate of r(t) liters per minute, where t is measured in minutes. What does the integral ∫ₐᵇ r(t) dt represent in this context?

3. The velocity of a particle moving along a line is given by v(t) meters per second. Explain the difference between ∫₀⁵ v(t) dt and the total distance traveled by the particle from t = 0 to t = 5.

...and 4 more questions

Educational Video

Interpreting definite integral as net change | AP Calculus AB | Khan Academy

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