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
![### Evaluating Integrals
#### Tasks:
a. **Evaluate**
\[ \int \frac{x}{\sqrt{x+9}} \, dx \]
using integration by parts.
b. **Evaluate**
\[ \int \frac{x}{\sqrt{x+9}} \, dx \]
using substitution.
c. **Verify** that your answers to parts (a) and (b) are consistent.
---
### Multiple Choice Question:
Use the integration by parts formula. Choose the correct answer.
- **A.**
\[ 2x\sqrt{x+9} - \int 2\sqrt{x+9} \, dx \]
- **B.**
\[ 2x\sqrt{x+9} - \int \frac{2}{\sqrt{x+9}} \, dx \]
- **C.**
\[ 2x\sqrt{x+9} + \int 2\sqrt{x+9} \, dx \]
- **D.**
\[ 2x\sqrt{x+9} + \int \frac{2}{\sqrt{x+9}} \, dx \]
**Correct Answer:** B.
\[ 2x\sqrt{x+9} - \int \frac{2}{\sqrt{x+9}} \, dx \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1913c9c-da59-4e5e-af1e-78b6351c7d9b%2F17809918-d4d7-46d4-a574-0f55e72a2d1f%2F01tf7bb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluating Integrals
#### Tasks:
a. **Evaluate**
\[ \int \frac{x}{\sqrt{x+9}} \, dx \]
using integration by parts.
b. **Evaluate**
\[ \int \frac{x}{\sqrt{x+9}} \, dx \]
using substitution.
c. **Verify** that your answers to parts (a) and (b) are consistent.
---
### Multiple Choice Question:
Use the integration by parts formula. Choose the correct answer.
- **A.**
\[ 2x\sqrt{x+9} - \int 2\sqrt{x+9} \, dx \]
- **B.**
\[ 2x\sqrt{x+9} - \int \frac{2}{\sqrt{x+9}} \, dx \]
- **C.**
\[ 2x\sqrt{x+9} + \int 2\sqrt{x+9} \, dx \]
- **D.**
\[ 2x\sqrt{x+9} + \int \frac{2}{\sqrt{x+9}} \, dx \]
**Correct Answer:** B.
\[ 2x\sqrt{x+9} - \int \frac{2}{\sqrt{x+9}} \, dx \]
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