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Math Help - Can you hlep me with this?

  1. #1
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    Cool Can you hlep me with this?

    If f is continuous on [2,4] and the integral of f(x) dx from 2 to 4 is equal to 7, explain why f(c) is greater than or equal to 3 for some c in [2,4].
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Susie38
    If f is continuous on [2,4] and the integral of f(x) dx from 2 to 4 is equal to 7, explain why f(c) is greater than or equal to 3 for some c in [2,4].
    let f(x) is less than 3 for all points in [2,4]
    hence integral of f(x)dx from 2 to 4 will be less than integral of 3dx from 2 to 4
    but integral of 3dx from 2 to 4 is 6
    which contradicts the condition
    actully f(x) should be greater than 3.5 for some c if it is changing with x
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