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Math Help - Some Form of integral question! who knows

  1. #1
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    Some Form of integral question! who knows

    Let F=[2 \sin (x) \cos (x), 0, 2z] and r(t)=[\cos (t),\sin (t),t]

    Calculate \int_0^{2\pi} F(r(t)).r(t)dt
    Last edited by CaptainBlack; December 6th 2008 at 01:12 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Ash_underpar View Post
    Let F=[2 \sin (x) \cos (x), 0, 2z] and r(t)=[\cos (t),\sin (t),t]

    Calculate \int_0^{2\pi} F(r(t)).r(t)dt
    I'm not sure your notation makes sense as it is. F is a function of two(?) (real?) variables taking values in \mathbb(R)^3, and r is a function of a single (real?) variable taking values in \mathbb(R)^3, so F(r(t)) is not properly defined. I expect with a bit of effort we could make some sort of guess about what this is supposed to denote but it would be better if you sorted it out.

    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    I'm not sure your notation makes sense as it is. F is a function of two(?) (real?) variables taking values in \mathbb(R)^3, and r is a function of a single (real?) variable taking values in \mathbb(R)^3, so F(r(t)) is not properly defined. I expect with a bit of effort we could make some sort of guess about what this is supposed to denote but it would be better if you sorted it out.

    CB
    I figured that F(r(t)) could be worked out by using the vector format and taking xi,yj,zk to equal the values of the three points of r(t) taking the y value as 0y, and then integrate the dot product between this value and r(t), which is what i am stuck on but the question i have been set is written exactly as i have put on here.

    In textbooks i have used, F seems to be denoted by F(r), but i don't know if thats actually a completely separate value!
    Last edited by Ash_underpar; December 7th 2008 at 08:20 AM.
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