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Thread: how find the formula

  1. #1
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    how find the formula

    I'm really stuck on this question, I have tried it and read through my notes but can't find a way to solve it. Help would be greatly appreciated.

    A linear function f(x) passes through a point (-2,3) and agrees with the condition f(x)dx = -44. What is the formula?

    ps: sorry for the paint drawing. I didnt know how else to show it.
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  2. #2
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    Quote Originally Posted by JQ2009 View Post
    I'm really stuck on this question, I have tried it and read through my notes but can't find a way to solve it. Help would be greatly appreciated.

    A linear function f(x) passes through a point (-2,3) and agrees with the condition f(x)dx = -44. What is the formula?

    ps: sorry for the paint drawing. I didnt know how else to show it.
    $\displaystyle y = mx+b$

    point $\displaystyle (-2,3)$ is on the line ...

    $\displaystyle 3 = -2m+b$

    $\displaystyle b = 2m+3$


    $\displaystyle \int_2^4 mx+b \, dx = -44$

    $\displaystyle \int_2^4 mx + (2m+3) \, dx = -44$

    evaluate the definite integral, solve for $\displaystyle m$ ... calculate $\displaystyle b$.
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