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Math Help - Average Value

  1. #1
    VkL
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    Average Value

    If the average value of f on the interval 2 < or = x < = 5 is 4, Find integral form 2 to 5 of (3(f(x) + 2)dx
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    Quote Originally Posted by VkL View Post
    If the average value of f on the interval 2 < or = x < = 5 is 4, Find integral form 2 to 5 of (3(f(x) + 2)dx
    The "average" value of a function, f, on the interval a\le x\le b is \frac{\int_a^b f(x)dx}{b-a} so knowing that the average of f on [tex]a\le x\le 5[/itex] is 4 tells you that \frac{\int_2^5 f(x)dx}{3}= 4 so \int_2^5 f(x)dx= 4(3)= 12.
    \int_2^5 (3f(x)+ 2)dx= 3\int_2^5 f(x)dx+ 2\int_2^5 dx.
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