AP Calculus AB Integration by Substitution Quiz: 10 Questions with Explanations

AP Calculus AB math quiz: Integration by Substitution – Maths PDF

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This u substitution quiz for AP Calculus AB covers integration by substitution (Common Core AP CALC AB 6.9, AP CALC AB 6.10, AP CALC AB 6.11, AP CALC AB 6.12, AP CALC AB 6.14), with a free PDF to print.

Test yourself on integration by u-substitution for indefinite and definite integrals, long division, completing the square and choosing a technique with 10 multiple-choice questions. Pick one answer for each question, then read the explanation to see why it is right and which common mistake the other choices represent.

AP Calculus AB · Common Core State Standards: AP CALC AB 6.9, AP CALC AB 6.10, AP CALC AB 6.11, AP CALC AB 6.12, AP CALC AB 6.14

U substitution quiz: 10 questions

Question 1

For \(\int 2x(x^{2}+3)^{5}\,dx\), which substitution works best?

Question 2

What is \(\int 2x(x^{2}+3)^{5}\,dx\)?

Question 3

What is \(\int e^{2x}\,dx\)?

Question 4

Converting limits.

In \(\int_{0}^{1}2x(x^{2}+1)^{3}\,dx\) with \(u=x^{2}+1\), what are the new limits?

Question 5

What is \(\int\frac{1}{x}\ln x\,dx\)?

Question 6

What is \(\int\sin(4x)\,dx\)?

Question 7

The area under x√(x² + 1).

What is \(\int_{0}^{\sqrt{3}}x\sqrt{x^{2}+1}\,dx\)?

Question 8

What is \(\int\tan x\,dx\)?

Question 9

Which technique is best for \(\int\frac{x^{2}+1}{x+1}\,dx\)?

Question 10

f(x) = 1/(x² + 1) (blue) and an antiderivative (green).

What is \(\int\frac{1}{x^{2}+1}\,dx\)?

Remember

Let u = g(x) and du = g′(x) dx, then the integral becomes the integral of f(u) du.
Adjust constant factors: if du is off by a constant, divide or multiply to compensate.
For definite integrals, change the limits to u-values or return to x before evaluating.
Use long division for improper rational functions and completing the square for irreducible quadratics.

How to use this u substitution quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

Download the u substitution quiz as a PDF with the button below and keep it with your notes.

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