   Chapter 8.5, Problem 9CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
3 views

# Use the temperature function T in Example 9 to find the average temperature from 9 A.M. to noon.

To determine

To calculate: The average temperature from 9 A.M to noon, when the expression for temperature is given as T=72+18sinπ(t8)12.

Explanation

Given Information:

The provided expression for temperature is given as T=72+18sinπ(t8)12.

Formula used:

Formula for average value of a provided function f(x) for [a,b].

Average value=1baabf(x)dx

Formula for definite integral of sinudu.

absinnudu=[cosnun]ab

Formula for integral of un.

undu=un+1n+1+C

Calculation:

Since, noon is known as 12, so noon is at t=12, corresponding to t=9 at 9 A.M. Therefore, interval can be mathematically written as:

[a,b]=[9,12]

Write the average temperature with the help of provided function.

Average temperature=1129912[72+18sinπ(t8)12]dt

Use the above integral formulae to find integral of above expression

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