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Math Help - Need help with integral problem

  1. #1
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    Need help with integral problem



    my answer is the one in the box. really Im not sure what Im doing after I find the main integral so any help would be appreciated. i think i got the integral correct buuuuut... who knows.
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  2. #2
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    Hello, pseizure2000!

    Consider the function: f(x) \:=\:x^3 + 5\sqrt{x}
    Let F(x) be the antiderivative of f(x) with F(1) = -6.

    Then: F(x) \:=\:\boxed{\frac{1}{4}x^4 +\frac{10}{3}x^{\frac{3}{2}} + 6} . . . . no

    My answer is the one in the box.
    Check it out yourself . . . Does F(1) = -6 ?

    When we integrate, we get: . F(x) \:=\:\frac{1}{4}x^4 + \frac{10}{3}x^{\frac{3}{2}} + C .[1]

    We are told that: . F(1) = -6
    . . That is, when x = 1,\:F(1) = -6

    Substitute into [1]: . \frac{1}{4}\left(1^4\right) +\frac{10}{3}\left(1^{\frac{3}{2}}\right) + C \;=\;-6\quad\Rightarrow\quad C \:=\:-\frac{115}{12}

    Therefore: . F(x) \;=\;\frac{1}{4}x^4 + \frac{10}{3}x^{\frac{3}{2}} - \frac{115}{12}

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