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Math Help - Definite integral of parametric equation

  1. #1
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    Definite integral of parametric equation

    <br /> <br />
\int^1_{-1} {(4ti+2t^3j-\sqrt[3]{t}k)}  dt<br /> <br /> <br /> <br />

    Sadly, I'm supposed to tutor someone in calculus III tomorrow and am going through the homework tonight and came across this. No idea how to solve whatsoever. Can someone point me in the right direction?

    Thank in advance.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Negativ View Post
    <br /> <br />
\int^1_{-1} {(4ti+2t^3j-\sqrt[3]{t}k)}  dt<br /> <br /> <br /> <br />

    Sadly, I'm supposed to tutor someone in calculus III tomorrow and am going through the homework tonight and came across this. No idea how to solve whatsoever. Can someone point me in the right direction?

    Thank in advance.
    are i=e_1=(1,0,0) etc?
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  3. #3
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    Yes, they are unit vectors. 1,0,0 ; 0,1,0 ; 0,0,1
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Negativ View Post
    Yes, they are unit vectors. 1,0,0 ; 0,1,0 ; 0,0,1
    What's the problem then? We integrate a vector valued function coordinate-wise.
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  5. #5
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    Meaning that I integrate them all separately? (And if so, I don't understand how to integrate the last piece since I don't know what -1^{4/3} is.
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  6. #6
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    Still unclear on this. Any help appreciated.
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  7. #7
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    Quote Originally Posted by Negativ View Post
    <br /> <br />
\int^1_{-1} {(4ti+2t^3j-\sqrt[3]{t}k)}  dt<br /> <br /> <br /> <br />

    Sadly, I'm supposed to tutor someone in calculus III tomorrow and am going through the homework tonight and came across this. No idea how to solve whatsoever. Can someone point me in the right direction?

    Thank in advance.
    \int^1_{-1} {(4t\vec{i}+2t^3\vec{j}-\sqrt[3]{t}\vec{k})}= \left(\int_{-1}^1 4t  dt<br />
\right)\vec{i}+ \left(\int_{-1}^1 2t^3 dt\right)\vec{j}- \left(\int_{-1}^1 t^{1/3} dt\right)\vec{k}
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  8. #8
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    First two are zero, unsure on last one is what I was unclear on. Sorry for not being specific.
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  9. #9
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by Negativ View Post
    First two are zero, unsure on last one is what I was unclear on. Sorry for not being specific.
    It is 0 as well.

    Since t^{\frac{1}{3}} is symetric
    Last edited by 11rdc11; June 10th 2010 at 07:46 PM.
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