Use integration by parts to evaluate the definite integral: 97.18 In (8r+4) dr = 8.92 HINT: You might want to us

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.
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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