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Math Help - Find y in terms of x

  1. #1
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    Find y in terms of x

    Hello,

    Ive been having trouble solving this problem.
    I could really use help

    In this case find y in terms of x

    dy/dx= (√x+5)^2

    Thank you in advance

    Rob
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  2. #2
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     \frac{dy}{dx}= (\sqrt{x}+5)^2

     y= \int(\sqrt{x}+5)^2~dx

    I suggest expanding the brackets and integrating each term individually.

     y= \int x+10\sqrt{x}+25~dx

    Can you take it from here?
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  3. #3
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    Quote Originally Posted by pickslides View Post
     \frac{dy}{dx}= (\sqrt{x}+5)^2

     y= \int(\sqrt{x}+5)^2~dx

    I suggest expanding the brackets and integrating each term individually.

     y= \int x+10\sqrt{x}+25~dx

    Can you take it from here?
    Dear Pickslides thans for the reply but can you show me how its solved?

    Ive got the answers but dont know how to get that answer.

    Thanks
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  4. #4
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     y= \int x+10\sqrt{x}+25~dx

     y= \int x~dx+\int 10\sqrt{x}~dx+\int 25~dx


    Now use the following rule for each part.

     \int x^n~dx = \frac{x^{n+1}}{n+1}+c

    for each part.

    Spoiler:
    y= \frac{x^2}{2}+\frac{20x^{\frac{3}{2}}}{3}+25x+c
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  5. #5
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    Quote Originally Posted by Oasis1993 View Post
    Dear Pickslides thans for the reply but can you show me how its solved?

    Ive got the answers but dont know how to get that answer.

    Thanks
    What more is needed? You're expected to realise that \sqrt{x} = x^{1/2} and then use the usual rule for integrating x^n.
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