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Math Help - Line Integral

  1. #1
    Member Em Yeu Anh's Avatar
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    Red face Line Integral

    Evaluate \int_Csinxdx+cosydy where C is the top half of the circle x^2+y^2=4 from (2,0) to (-2,0) and the line segment from (-2,0) to (-3,2).

    Haven't done vector calc in awhile, still a little bit rusty, can someone assist me with getting the parametric equations for the line segment?
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    The line segment from p_1 to p_2 can be parametrized as r(t)=(1-t)p_1+tp_2, 0 \leq t \leq 1.
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  3. #3
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by Em Yeu Anh View Post
    Evaluate \int_Csinxdx+cosydy where C is the top half of the circle x^2+y^2=4 from (2,0) to (-2,0) and the line segment from (-2,0) to (-3,2).

    Haven't done vector calc in awhile, still a little bit rusty, can someone assist me with getting the parametric equations for the line segment?

    For the circle let

    x=2\cos{t} and dx = -2\sin{t}

    y =2\sin{t} and dy = 2\cos{t}

    Now sub these values for

    \int_Csinxdx+cosydy

    and you get

    C_1 = \int^{\pi}_{0} \bigg(-2\sin{t}\sin{(2\cos{t})}+ 2\cos{t}\cos{(2\sin{t})}\bigg)dt

    For C_2

    x = -2 -t and dx= -1

    y =2t and dy = 2

    and then just sub in like before.
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