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Thread: Confused About Finding Function based on the Integral

  1. #1
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    Confused About Finding Function based on the Integral

    Confused About Finding Function based on the Integral-capture.png

    I know that the function that is based on the integral is just done by taking the integral with our rules which get me (5/3)x^3 - 2x^2, but im not sure how im suppose to find the C value based on what's given?

    Any guidance/explanation would be nice
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  2. #2
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    Re: Confused About Finding Function based on the Integral

    This is a definite integral. There is no added constant

    $\begin{align*}
    &\displaystyle \int_2^x (5t^2 - 4t)~dt = \\
    &\left . \dfrac 5 3 t^3 - 2t^2 \right |_2^x = \\
    &\left(\dfrac 5 3 x^3 - 2 x^2\right) - \left(\dfrac 5 3 2^3 - 2(2)^2\right) = \\
    &\left(\dfrac 5 3 x^3 - 2 x^2\right) - \left(\dfrac{40}{3} - 8\right ) = \\
    &\dfrac 5 3 x^3 - 2 x^2 - \dfrac{16}{3}
    \end{align*}$
    Thanks from HallsofIvy and lc99
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