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Math Help - Line Integral

  1. #1
    Member Altair's Avatar
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    Line Integral

    I have to find line integral for F = [y^3, x^3] , C the parabola y=5x^2 from A: (0,0) to B(2,20).

    I have made the parametric equations to be x=t and y=5t^2. What I dont understand is that in order to integrate I need just one value of a and b , i.e. the limits. How do I chnage the A and B coordinates in the form of limits ?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Altair View Post
    I have to find line integral for F = [y^3, x^3] , C the parabola y=5x^2 from A: (0,0) to B(2,20).

    I have made the parametric equations to be x=t and y=5t^2. What I dont understand is that in order to integrate I need just one value of a and b , i.e. the limits. How do I chnage the A and B coordinates in the form of limits ?
    t goes from 0 up to 2

    can you finish now?
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  3. #3
    Member Altair's Avatar
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    That is what I am asking actually. How can you tell that it goes from 0 to 2 ?
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  4. #4
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    Quote Originally Posted by Altair View Post
    That is what I am asking actually. How can you tell that it goes from 0 to 2 ?
    (0, 0) \Rightarrow x = 0 and y = 0. But x = t \Rightarrow 0 = t. Check: y = 5 t^2 = 0.

    (2, 20) \Rightarrow x = 2 and y = 20. But x = t \Rightarrow 2 = t. Check: y = 5 t^2 = 5 (2)^2 = 20.
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