Determine if the improper integral is convergent or divergent, and calculate its value if it is convergent. 9x 9e dx Calculate the value of the improper integral. Select the correct choice below and, if necessary, fill in the answer box to complete y 00 DA. [₁.-"&x=|| Js 9x xdx= 0 OB. The improper integral diverges.
Determine if the improper integral is convergent or divergent, and calculate its value if it is convergent. 9x 9e dx Calculate the value of the improper integral. Select the correct choice below and, if necessary, fill in the answer box to complete y 00 DA. [₁.-"&x=|| Js 9x xdx= 0 OB. The improper integral diverges.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Improper Integrals: Convergence or Divergence
**Problem Statement:**
Determine if the improper integral is convergent or divergent, and calculate its value if it is convergent.
\[
\int_{0}^{\infty} e^{-9x} \, dx
\]
---
**Instructions:**
Calculate the value of the improper integral. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
**Options:**
- **A.** \[
\int_{0}^{\infty} e^{-9x} \, dx = \boxed{}
\]
- **B.** The improper integral diverges.
**Note:** In the problem, the integral represents an improper integral due to the infinite limit. Analyzing this integral typically involves checking the behavior of the integrand as \( x \) approaches infinity and whether the integral converges to a finite number or diverges.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F756689fc-aa25-4045-a342-f553545a40f2%2Fcfe0b9a5-f82d-4ed5-af07-060630a8677d%2F2a4c3sb_processed.png&w=3840&q=75)
Transcribed Image Text:### Improper Integrals: Convergence or Divergence
**Problem Statement:**
Determine if the improper integral is convergent or divergent, and calculate its value if it is convergent.
\[
\int_{0}^{\infty} e^{-9x} \, dx
\]
---
**Instructions:**
Calculate the value of the improper integral. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
**Options:**
- **A.** \[
\int_{0}^{\infty} e^{-9x} \, dx = \boxed{}
\]
- **B.** The improper integral diverges.
**Note:** In the problem, the integral represents an improper integral due to the infinite limit. Analyzing this integral typically involves checking the behavior of the integrand as \( x \) approaches infinity and whether the integral converges to a finite number or diverges.
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