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Math Help - average value of a function

  1. #1
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    average value of a function

    the temperature (in Celsius) t hours after 9am was modeled by the function T(t) = 20 + 6\sin \frac{\pi t}{12} find the average temperature from 9am to 9pm.

    answer: about 24 C
    what I did: \frac{1}{21-9} \int_9^{21} + 6\sin \frac{\pi t}{12}dt which gives me about 17.299
    Last edited by superdude; July 21st 2009 at 10:53 AM. Reason: fixed latex
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  2. #2
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    Hello superdude
    Quote Originally Posted by superdude View Post
    the temperature (in Celsius) t hours after 9am was modeled by the function T(t) = 20 + 6\sin \frac{\pi t}{12} find the average temperature from 9am to 9pm.

    answer: about 24 C
    what I did: \frac{1}{21-9} \int_9^21 + 6\sin \frac{\pi t}{12}dt which gives me about 17.299

    the upper limit of integration is suppose to be 21 but (I believe) Latex is limited to 1 character
    Read the question carefully! The values of t are measured after 9 am, so the limits of the integral are 0 to 12, not 9 to 21.

    Incidentally you can get LaTeX to accept more that one character for the limit of an integral by enclosing the character string in {...} as you have done with \frac{...}{...}. Like this:

    \int_0^{12}(20 +6\sin \frac{\pi t}{12})dt

    Hover the mouse over the LaTeX image, and the code will appear; or click on it and it'll pop up in a separate window. Try it!

    Grandad
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  3. #3
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    got it, thanks.
    Is the reason I integrate from 0 to 12 because the function/data is undefined every where else? I understand why it should be this, I am having trouble coming up with a rule so I don't make the same mistake in another question.
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  4. #4
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    Hello superdude
    Quote Originally Posted by superdude View Post
    got it, thanks.
    Is the reason I integrate from 0 to 12 because the function/data is undefined every where else? ...
    No, it's because the value of t is defined as follows:
    Quote Originally Posted by superdude View Post
    the temperature (in Celsius) t hours after 9am was modeled by the function T(t) = 20 + 6\sin \frac{\pi t}{12} ...
    and the question asks for
    Quote Originally Posted by superdude View Post
    ... the average temperature from 9am to 9pm.
    So the values of t you need are from 0 to 12 (9am + 0 hours to 9am + 12 hours).

    Grandad
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