Unit 8: Applications of Integration FRQ & MCQ Walkthrough

This video reviews AP Calculus AB Unit 8 multiple‑choice and free‑response questions involving accumulation, motion, area, volume, and applications of integrals, both with and without Desmos.

Summary

Unit 8 connects integrals to real‑world interpretations such as average value, motion (position, velocity, acceleration), area between curves, volume, and arc length. In this video I walk you through how to solve multiple FRQs and MCQs specifically from Unit 8. I'll emphasize proper justification, notation, and reasoning, which are critical for earning full credit on AP free‑response questions.

Key Takeaways

• Position is found using initial position plus the integral of velocity.

• Total distance traveled requires integrating the absolute value of velocity.

• Speed increases when velocity and acceleration have the same sign.

• Acceleration is negative when the velocity graph is decreasing.

• Trapezoidal sums can be computed as the average of left and right endpoint sums.

• Relative extrema for a differentiable function imply where a derivative must equal zero.

• Volume with known cross‑sections uses area functions integrated over an interval.

• When using Desmos, correct integral notation and units are required for credit on FRQs.

Transcript

 Welcome back everybody. Mr. Antonucci here, and in this video we’re going to go over some multiple‑choice and free‑response questions from AP Calculus Unit 8. We’re going to look at questions that involve using Desmos as well as those where Desmos is not permitted. Let’s go ahead and jump in.

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