Category: Lectures (Page 3 of 9)

Today’s quiz covered the topic of improper integrals. The first improper integral uses a function, \(f(x) = \frac{2}{\sqrt{x-3}}\), that has a vertical asymptote at \(x=3\). This \(x\)-value is also one of our bounds, which is what makes this an improper integral.

In today’s quiz, we tackle the decomposition of a fraction with a denominator that has both an irreducible quadratic factor (\(x^2+9\)) and a repeated linear factor \((x-3)^2\). Here at the start, it is crucial to make sure that we set up the correct decomposition by noting two important signals: the degree of the denominator and the number of factors.

Today’s quiz consisted of a single indefinite integral with several guiding questions on navigating the process of Partial Fraction Decomposition.