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Math Help - Integral Mean Value Theorem

  1. #1
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    Integral Mean Value Theorem

    Can someone show me how to do this... Find a value o c that satisfies the conlusion of the Integral Mean Value Theorem.

    3X^2(=8) on [0,2]

    I know the answer is 2/squareroot(3), and it is solved by the quadratic formula, but do not know how to get that.

    I also know that f(C)=4 OR 3C^2 = 4.
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  2. #2
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    Quote Originally Posted by gammaman View Post
    Can someone show me how to do this... Find a value o c that satisfies the conlusion of the Integral Mean Value Theorem.

    3X^2(=8) on [0,2]

    I know the answer is 2/squareroot(3), and it is solved by the quadratic formula, but do not know how to get that.

    I also know that f(C)=4 OR 3C^2 = 4.
    You need f(c) = \frac{1}{2-0}\int_0^2 3x^2 dx
    Therefore, 3c^2 = \frac{1}{2}\int_0^2 3x^2 dx

    Now solve for c after evaluating the RHS.
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    Ok but how do I get the answer?
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    Quote Originally Posted by gammaman View Post
    I thought that would be solving using the Integral Mean Value Theorem? I want to know how to get the value for c.
    That is exactly how you get that number. After you evaluate the integral on the RHS you get a number and so you have 3c^2 = \text{number}. This is an equation of c and so you can solve this equation for c.
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  5. #5
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    But what about the quadratic equation? Do I need that?
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    Quote Originally Posted by gammaman View Post
    But what about the quadratic equation? Do I need that?
    Solving 3 c^2 = \text{number} using the quadratic equation is like killing a fly with an elephant gun.
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