This ap calculus integration quiz asks 10 multiple-choice questions on integration and accumulation of change, and each answer comes with a short explanation.
Ten multiple-choice questions check the main ideas of AP Calculus AB Unit 6: antiderivatives, Riemann sums, properties of definite integrals, the Fundamental Theorem of Calculus, u-substitution and accumulation. Choose the single best answer for each question.
Find \(\int (4x^{3}-2x)\,dx\).
The rectangles shown are used to estimate \(\int_{0}^{4}(x^{2}+1)\,dx\). What is the value of this left Riemann sum?
A continuous function \(f\) is decreasing on \([0,6]\). How does a right Riemann sum with 3 equal subintervals compare with \(\int_{0}^{6} f(x)\,dx\)?
If \(\int_{2}^{5} f(x)\,dx=8\), what is \(\int_{5}^{2} 3f(x)\,dx\)?
Find \(\dfrac{d}{dx}\displaystyle\int_{0}^{x^{2}}e^{t}\,dt\).
Find \(\int 2x\cos\left(x^{2}\right)dx\).
The region under one arch of \(y=\sin x\) is shown. What is \(\int_{0}^{\pi}\sin x\,dx\)?
The graph of \(f\) is 2 on \([0,3]\) and then drops along a line to 0 at \(x=5\). What is \(\int_{0}^{5} f(x)\,dx\)?
Evaluate \(\displaystyle\int_{0}^{1}2xe^{x^{2}}\,dx\).
Water flows into a pool at the rate \(3t^{2}\) gallons per hour. How many gallons flow in between \(t=1\) and \(t=3\)?
🎉 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:
- AP Calculus AB Unit 6: Riemann sums, definite integrals, the Fundamental Theorem of Calculus, and antiderivative techniques.
- Left, right, midpoint and trapezoidal sums estimate \(\int_a^b f\,dx\); for \(f(x)=x^{2}+1\) on \([0,4]\) with \(n=4\) they give 18, 34, 25 and 26.
- FTC Part 1: \(\frac{d}{dx}\int_a^x f(t)\,dt=f(x)\). FTC Part 2: \(\int_a^b f\,dx=F(b)-F(a)\).
- In u-substitution, change the limits of integration along with the variable.
How to use this ap calculus integration quiz
Retake this ap calculus 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.