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Math Help - integration

  1. #1
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    integration

    I cant seem to get these 2 questions right.

    1) the problem:


    the attempted solution:


    * I rewrote the problem as 19\; \left( x^{3} \right)^{\frac{1}{2}}+14\left( x^{2} \right)^{\frac{1}{3}}
    and went from there. no dice.

    --------------------------------
    the second.
    problem:

    the attempted solution:
    I finished the division and got \frac{5}{y^{2}}+3y^{4}

    then proceded as normal but the resulting answer didnt work. Any hints? thanks a bunch.
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  2. #2
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    Try breaking your first integral up into 2 separate integrals.

    If you do that, you will have 19 times the integral of x^{3/2}+14 times the integral of x^{2/3}.

    Those should be pretty easy to solve then.

    You can break up the 2nd integral into 2 integrals as well too.
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  3. #3
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    Quote Originally Posted by Evan.Kimia View Post
    I cant seem to get these 2 questions right.

    1) the problem:


    the attempted solution:


    * I rewrote the problem as 19\; \left( x^{3} \right)^{\frac{1}{2}}+14\left( x^{2} \right)^{\frac{1}{3}}
    and went from there. no dice.

    --------------------------------
    the second.
    problem:

    the attempted solution:
    I finished the division and got \frac{5}{y^{2}}+3y^{4}

    then proceded as normal but the resulting answer didnt work. Any hints? thanks a bunch.
    Hi Evan.Kimia,

    \sqrt{x^3}=x^{(3)\frac{1}{2}}=x^{\frac{3}{2}}

    Now, to integrate that, increase the power by one and divide by the new power.
    Integrate the second term in the same way.

    \sqrt[3]{x^2}=x^{\frac{2}{3}}

    For the second one, write \frac{5}{y^2} as 5y^{-2}

    Use the same procedure...increase the power by one and divide by the new power.
    Of course, this time you must evaluate the definate integral.
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  4. #4
    Super Member
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    Quote Originally Posted by Evan.Kimia View Post
    I cant seem to get these 2 questions right.

    1) the problem:


    the attempted solution:
    <.. what's this

    * I rewrote the problem as 19\; \left( x^{3} \right)^{\frac{1}{2}}+14\left( x^{2} \right)^{\frac{1}{3}}
    and went from there. no dice.

    --------------------------------
    the second.
    problem:

    the attempted solution:
    I finished the division and got \frac{5}{y^{2}}+3y^{4}

    then proceded as normal but the resulting answer didnt work. Any hints? thanks a bunch.
    \int 19 (\left( x^{3} \right)^{\frac{1}{2}}+14\left( x^{2} \right)^{\frac{1}{3}})dx= \left [ 19\frac{2}{5}x^{\frac{5}{2}}+14\frac{3}{5}x^{\frac  {5}{3}} \right ]

    \int_{1}^{2}\left (5y^{-2}+3y^4  \right )dy=\left [ -5y^{-1}+\frac{3}{5}y^{5} \right ]_{1}^{2}=(\frac{-5}{2}+\frac{96}{5})-(-5+\frac{3}{5})
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  5. #5
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    Ah, thank you everyone, i caught my stupid mistakes. happy easter.
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