number 3 thank you **Question 3: Improper Riemann Integral Analysis**Consider the integral:\[\int_{2}^{3} \frac{1}{\sqrt{3-x}} \, dx\]**Task:**- **Explain why** this is an improper Riemann integral.- **Determine** whether this improper integral is convergent or divergent, and if it is convergent, **calculate** the value.---**Explanation:**An integral is considered improper if it involves infinities in the limits of integration or if the integrand approaches infinity within the interval of integration. The function \(\frac{1}{\sqrt{3-x}}\) becomes problematic at \(x = 3\) because the denominator \(\sqrt{3-x}\) approaches zero, causing the integrand to approach infinity. Thus, the integral is improper at the upper limit of integration.**Convergence Analysis:**To determine convergence, analyze the behavior of the integral as it approaches the problematic point (i.e., as \(x\) approaches 3 from the left). Evaluate the limit of the integral from 2 to a value approaching 3.**Calculation:**1. Find \(\lim_{{b \to 3^-}} \int_{2}^{b} \frac{1}{\sqrt{3-x}} \, dx\).2. If the limit exists and is finite, the integral is convergent; otherwise, it is divergent.3. If convergent, calculate the finite value of the limit.This approach will aid in determining whether the integral is finite (convergent) or infinite (divergent).

Name: number 3 thank you **Question 3: Improper Riemann Integral Analysis**C
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: number 3 thank you **Question 3: Improper Riemann Integral Analysis**Consider the integral:\[\int_{2}^{3} \frac{1}{\sqrt{3-x}} \, dx\]**Task:**- **Explain why** this is an improper Riemann integral.- **Determine** whether this improper integral is co