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...
Related questions
Question
Solve 347
![# Chapter 3 | Techniques of Integration
## 3.7 Exercises
Evaluate the following integrals. If the integral is not convergent, answer "divergent."
**347.** \[
\int_{a}^{4} \frac{dx}{(x - 3)^2}
\]
**348.** \[
\int_{0}^{\infty} \frac{1}{4 + x^2} \, dx
\]
**349.** \[
\int_{0}^{2} \frac{1}{\sqrt{4 - x^2}} \, dx
\]
**350.** \[
\int_{0}^{1} \frac{1}{x \ln x} \, dx
\]
### Diagram Explanation:
There is a hand-drawn sketch near exercise 347. This sketch appears to be a rough graph of the function \(\frac{1}{(x-3)^2}\) along with a shaded region between \(x = 2\) and \(x = 4\), suggesting the area that is represented by the definite integral in exercise 347. A note indicating interval \([a,4]\) is also present, which is relevant to the limits of the integral.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03fd5f25-eded-4046-9c65-9e89b5e28b89%2Fdf7efea8-b3df-4230-bcae-53a828876ca4%2F6eqdiqa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Chapter 3 | Techniques of Integration
## 3.7 Exercises
Evaluate the following integrals. If the integral is not convergent, answer "divergent."
**347.** \[
\int_{a}^{4} \frac{dx}{(x - 3)^2}
\]
**348.** \[
\int_{0}^{\infty} \frac{1}{4 + x^2} \, dx
\]
**349.** \[
\int_{0}^{2} \frac{1}{\sqrt{4 - x^2}} \, dx
\]
**350.** \[
\int_{0}^{1} \frac{1}{x \ln x} \, dx
\]
### Diagram Explanation:
There is a hand-drawn sketch near exercise 347. This sketch appears to be a rough graph of the function \(\frac{1}{(x-3)^2}\) along with a shaded region between \(x = 2\) and \(x = 4\), suggesting the area that is represented by the definite integral in exercise 347. A note indicating interval \([a,4]\) is also present, which is relevant to the limits of the integral.
Expert Solution
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Given query is to find integral converging or diverging.
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