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Math Help - another question on line integral

  1. #1
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    another question on line integral

    another question on line integral
    i have to evaluate the line integral
    ∫c (xy)^2 dx + xy^2 dy
    where c is closed curve formed by x=1 and y^2=x

    for this question. i drew a diagram which has three sides.
    c1 : x=1, y=t, 0<t<1
    c2 : x=t, y=0, 0<t<1
    c3 : x=t , y=x^1/2 , 0<t<1

    the book says the answer is 4/15. but i keep getting wrong answers
    where did i make mistake??
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  2. #2
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    Quote Originally Posted by panda View Post
    another question on line integral
    i have to evaluate the line integral
    ∫c (xy)^2 dx + xy^2 dy
    where c is closed curve formed by x=1 and y^2=x

    for this question. i drew a diagram which has three sides.
    c1 : x=1, y=t, 0<t<1
    c2 : x=t, y=0, 0<t<1
    c3 : x=t , y=x^1/2 , 0<t<1

    the book says the answer is 4/15. but i keep getting wrong answers
    where did i make mistake??
    Just post what you did thus we can show the error.
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  3. #3
    Junior Member
    Joined
    Jun 2008
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    i just integrated each of them
    then i got
    c1= 1/3
    c2=0
    c3=9/20

    and then if i add them all together, i get 47/60 which is different to the answer given in the book.

    the parametric set that I've written(c1,c2 and c3)..did i do it right?
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