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Math Help - Average Value of a Number

  1. #1
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    Post Average Value of a Number

    Can someone please help me out with this problem? It is the last one I have for my calculus assignment due tomorrow! We haven't done anything like this in class, so I have NO idea what to do.

    Here is a link to a picture of the problem because I couldn't type it on here.

    http://img3.imageshack.us/img3/5082/mathfp5.jpg
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  2. #2
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    Quote Originally Posted by JollyJolly15 View Post
    Can someone please help me out with this problem? It is the last one I have for my calculus assignment due tomorrow! We haven't done anything like this in class, so I have NO idea what to do.

    Here is a link to a picture of the problem because I couldn't type it on here.

    http://img3.imageshack.us/img3/5082/mathfp5.jpg

    The average value of a Riemann-integrable functuon f(x) over an interval (a,b)\,,\,a<b is given by \frac{1}{b-a}\int\limits^b_af(x)\,dx

    In your case, note that \sec^2x=(\tan x)' , so the integral of that function is pretty easy...

    Tonio
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  3. #3
    Member grgrsanjay's Avatar
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    Cool simple

    we should do differentiation or integration??
    if its deferenciation then
    use the product principle rule
    e^3tanx+1 * d/dx sec^2x + sec^2x * d/dx e^3tanx+1
    = e^3tanx+1 * 2secx(secxtanx) + sec^2x * e^3tanx+1(3sec^2x)
    then simplyfy it and substitute x as 0 and x as 45 and then add the values and divide them by 2,
    you will get the answer
    Last edited by grgrsanjay; May 6th 2010 at 08:40 AM. Reason: more clear explanation
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  4. #4
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    Quote Originally Posted by grgrsanjay View Post
    we should do differentiation or integration??
    if its deferenciation then
    use the product principle rule
    e^3tanx+1 * d/dx sec^2x + sec^2x * d/dx e^3tanx+1
    = e^3tanx+1 * 2secx(secxtanx) + sec^2x * e^3tanx+1(3sec^2x)
    then simplyfy it and substitute x as 0 and x as 45 and then add the values and divide them by 2,
    you will get the answer
    Tonio had already said that it was an integration

    If you needed to find the average of a finite list of numbers, you would add them all up and divide by the "number of numbers". With a continuous function that "adding" becomes integrating.
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