This ap calculus applications integration quiz asks 10 multiple-choice questions on applications of integration, and each answer comes with a short explanation.
Ten multiple-choice questions check average value, motion, area between curves, volumes and accumulation. Pick one answer for each question, then read the explanation to see the typical mistake behind each wrong choice.
What is the area of the shaded region between \(y=2x\) and \(y=x^{2}\)?
This region is revolved about the \(x\)-axis. Which integral gives the volume?
The graph shows the rate in \(10-t\) and the rate out \(2+t\) for the amount in a tank. At which time on \(0\le t\le 8\) is the amount greatest?
The graph shows the velocity of a particle for \(0\le t\le 4\). What is the total distance traveled?
🎉 Quiz complete!
How does this quiz work?
Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.
What should you review before the quiz?
Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.
Remember:
- Average value: \(\frac{1}{b-a}\int_{a}^{b}f(x)\,dx\).
- Area between curves: integrate top minus bottom, or right minus left.
- Volume with cross sections: \(\int A(x)\,dx\); washers: \(\pi\int(R^{2}-r^{2})\,dx\).
- Net change: \(A(b)=A(a)+\int_{a}^{b}A^{\prime}(t)\,dt\).
How to use this ap calculus applications integration quiz
Retake this ap calculus applications integration quiz until every answer is right, then move on to the worksheet and the test.
See every chapter on the AP Calculus AB math page.