Question

question 4 (1 point) let p be a constant. for what value(s) of p is the integral
∫₁⁵ 1/(x - p) dx improper? (i.e. for what p value(s) would we need to use the \improper integrals - type 2\ techniques to solve?) p = 1 and p = 5 only. p = 0 only. this integral is never improper. all p on the interval 1,5 only. the integral is improper for all p on (-∞, ∞).

Explanation:

Step1: Define Type 2 improper integral

A Type 2 improper integral has a discontinuity in the interval of integration.

Step2: Check denominator at bounds

The integrand is $\frac{1}{x-p}$. At $x=1$, denominator is $1-p$; at $x=5$, denominator is $5-p$. For discontinuity in $[1,5]$, set $1-p=0$ or $5-p=0$.

Step3: Solve for p

$1-p=0 \Rightarrow p=1$; $5-p=0 \Rightarrow p=5$.

Answer:

p = 1 and p = 5 only.