Calculus II, Spring 2024 (http://www.math.nthu.edu.tw/˜ wangwc/) Thomas’ Calculus Early Transcendentals 13ed

Study guide for quiz 01

Quiz problems include both the lecture contents and homework problems.

1. Section 8.8:

Memorize the definitions of type I and type II improper integrals and study how to verify convergence/divergence of improper integrals from these definitions. You may need to review some techniques of integration, such as ”integration by parts”, etc..

2. Section 8.8:

Study the convergence/divergence of the improper integrals ∫_{a}^{∞} \frac{1}{x^{p}} dx (a > 0), ∫_{0}^{a} \frac{1}{x^{p}} dx,

∫_{c}^{c+a} \frac{1}{(x − c)^{p}} dx, and ∫_{c−a}^{c} \frac{1}{|x − c|^{p}} dx for p > 1, p = 1 and 0 < p < 1, respectively by

direct computation. Then memorize the results.