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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![### Question 11
Malachi has the following information about \( f(x) \):
- \( f(4) = 10 \)
- \( f(6) = 2 \)
- \(\int_{4}^{6} e^{-2x}f(x) \, dx = 18\)
**Evaluate:**
\[
\int_{4}^{6} e^{-2x}f'(x) \, dx = \_\_\_
\]
---
### Explanation
In this problem, we are given specific values of the function \( f(x) \) at certain points and an integral of \( e^{-2x}f(x) \). We are asked to evaluate the integral of \( e^{-2x}f'(x) \) over the same interval \([4, 6]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39ee8330-8a26-4cdb-b3ef-e7a0164aa18c%2F83a403ca-a018-4f47-9849-d886e537970e%2Fkp96hge_processed.png&w=3840&q=75)
Transcribed Image Text:### Question 11
Malachi has the following information about \( f(x) \):
- \( f(4) = 10 \)
- \( f(6) = 2 \)
- \(\int_{4}^{6} e^{-2x}f(x) \, dx = 18\)
**Evaluate:**
\[
\int_{4}^{6} e^{-2x}f'(x) \, dx = \_\_\_
\]
---
### Explanation
In this problem, we are given specific values of the function \( f(x) \) at certain points and an integral of \( e^{-2x}f(x) \). We are asked to evaluate the integral of \( e^{-2x}f'(x) \) over the same interval \([4, 6]\).
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