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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5.3 Q6) Hey! I need help with the following calc question, thank you!
![### Finding the Average Value of a Function
Given the task is to find the average value of the function over the given interval and to round the answer to two decimal places.
The function provided is:
\[ H(t) = 3.7 e^{0.5t} \]
The interval is:
\[ [0, 9] \]
To find the average value \( \overline{H} \) of a function \( H(t) \) over an interval \([a, b]\), use the formula:
\[ \overline{H} = \frac{1}{b-a} \int_{a}^{b} H(t) \, dt \]
In this case:
\[ a = 0 \]
\[ b = 9 \]
Thus the formula becomes:
\[ \overline{H} = \frac{1}{9-0} \int_{0}^{9} 3.7 e^{0.5t} \, dt \]
The problem involves evaluating this integral and then dividing by the length of the interval to find the average value. Ensure your final answer is rounded to two decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccd97de8-e10b-493c-b965-7d9287dd2ac4%2F42a717eb-a20b-40cf-b7c8-9a5662755dc2%2Fo8ok78_processed.png&w=3840&q=75)
Transcribed Image Text:### Finding the Average Value of a Function
Given the task is to find the average value of the function over the given interval and to round the answer to two decimal places.
The function provided is:
\[ H(t) = 3.7 e^{0.5t} \]
The interval is:
\[ [0, 9] \]
To find the average value \( \overline{H} \) of a function \( H(t) \) over an interval \([a, b]\), use the formula:
\[ \overline{H} = \frac{1}{b-a} \int_{a}^{b} H(t) \, dt \]
In this case:
\[ a = 0 \]
\[ b = 9 \]
Thus the formula becomes:
\[ \overline{H} = \frac{1}{9-0} \int_{0}^{9} 3.7 e^{0.5t} \, dt \]
The problem involves evaluating this integral and then dividing by the length of the interval to find the average value. Ensure your final answer is rounded to two decimal places.
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