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Math Help - mean value theorem

  1. #1
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    mean value theorem

    Can someone please show me or tell me why the Mean Value Theorem for integrals is a special case of the generalized Mean Value Theorem for integrals.

    Mean Value Theorem for Integrals: If f is continuous on [a,b], then there exists a point cE[a,b] such that f(c)(b-a)= inetgral of f from a to b.

    generalized Mean Value Theorem: If f is continuous on [a,b] and g is nonnegative Riemann integrable function on [a,b], then there exists a point cE[a,b] such that f(c) integral of g from a to b = integral of fg from a to b.
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  2. #2
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    Quote Originally Posted by summerset353 View Post
    Can someone please show me or tell me why the Mean Value Theorem for integrals is a special case of the generalized Mean Value Theorem for integrals.

    Mean Value Theorem for Integrals: If f is continuous on [a,b], then there exists a point cE[a,b] such that f(c)(b-a)= inetgral of f from a to b.

    generalized Mean Value Theorem: If f is continuous on [a,b] and g is nonnegative Riemann integrable function on [a,b], then there exists a point cE[a,b] such that f(c) integral of g from a to b = integral of fg from a to b.
    In the generalized Mean Value Theorem consider g(x)=1.
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