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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![**Example Problem: Integration by Parts**
Use integration by parts to evaluate the definite integral:
\[
\int_{8.92}^{97.18} \ln(8r + 4) \, dr = \, [ \text{Solution Box} \, ]
\]
**Hint:** You might want to use a substitution *before* you do integration by parts.
**Instructions:**
- Apply the method of integration by parts to solve the given definite integral.
- Report your answer accurate to four decimal places.
**Additional Information:**
Integration by parts is a technique based on the product rule for differentiation. It is useful for integrating the products of functions. For integrating a function of form \(\int u \, dv\), we use:
\[
\int u \, dv = uv - \int v \, du
\]
Consider making a substitution to simplify the integral before applying integration by parts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1f0f51f-f003-4ca2-9c03-b14a76478a3a%2F3d2e9e8d-294f-4915-b328-622577c8ab0d%2Fltfi0rq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example Problem: Integration by Parts**
Use integration by parts to evaluate the definite integral:
\[
\int_{8.92}^{97.18} \ln(8r + 4) \, dr = \, [ \text{Solution Box} \, ]
\]
**Hint:** You might want to use a substitution *before* you do integration by parts.
**Instructions:**
- Apply the method of integration by parts to solve the given definite integral.
- Report your answer accurate to four decimal places.
**Additional Information:**
Integration by parts is a technique based on the product rule for differentiation. It is useful for integrating the products of functions. For integrating a function of form \(\int u \, dv\), we use:
\[
\int u \, dv = uv - \int v \, du
\]
Consider making a substitution to simplify the integral before applying integration by parts.
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