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Thread: u-subsitution.

  1. #1
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    u-subsitution.

    I understand how to do it's just I don't understand what a certain part of my homewor kmeans.
    Using the method of u-substitution,

    $\displaystyle \(\displaystyle \int_{2}^{4} (5 x - 7)^{4} \, dx = \int_{a}^{b} f(u) \, du\) $

    where

    $\displaystyle u = 5x-7$ (enter a function of x)
    $\displaystyle du = 5$ dx (enter a function of x)
    $\displaystyle a =2$ (enter a number)
    $\displaystyle b =4$ (enter a number)
    $\displaystyle f(u) =?$ (enter a function of u).

    The value of the original integral is .
    What does f(u) mean? I plug in u for the values of x?
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  2. #2
    Junior Member bondesan's Avatar
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    Zanderist,

    When you have $\displaystyle f(x) = (5x-7)^4$ its clever to choose $\displaystyle 5x-7 = u$, because you are left with $\displaystyle (u)^4$, so $\displaystyle f(u) = u^4$ and $\displaystyle \int u^4 du = \frac{u^5}{5}$, which is "more simple" than the integral with respect of x.
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  3. #3
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    Recheck your upper and lower bounds.
    Quote Originally Posted by Zanderist View Post
    I understand how to do it's just I don't understand what a certain part of my homewor kmeans.
    What does f(u) mean? I plug in u for the values of x?
    $\displaystyle f(u)$ is the new integrand, the function which you have obtained in terms of $\displaystyle u$ after the substitution.
    I plug in u for the values of x?
    No, the whole point of the substitution was to get a new function that's easier to integrate.
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