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Math Help - solving line integral by bounded area

  1. #1
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    solving line integral by bounded area

    calculate \int_{c}Fdr where F(x,y)=(e^{x}-4ycos^{2}x)i+(2x-sin2x-ln(y^{2}+1))j and the curve C is y(x)=-\sqrt{1-x^{2}} where -1\leq x\leq1

    i closed this curve with y=0 and did double integral over the bounded area
    instead of caulculating the curve integral.

    in the photo it written that it wrong i dont know why?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: solving line integral by bounded area

    Quote Originally Posted by transgalactic View Post
    in the photo it written that it wrong i dont know why?


    Would you read a document presented in this way?
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  3. #3
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    Re: solving line integral by bounded area

    flipped it.
    is it ok ?
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  4. #4
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    Re: solving line integral by bounded area

    Your error is not completing the boundary- the integral around the semi-circle is equal to the integral over the area minus the integral along the x-axis.

    But the obvious way to do it is directly- use parametric equations: [itex]x= cos(\theta)[/itex], '[itex]y= sin(\theta)[/itex], [itex]dx= -sin(\theta)d\theta[/itex], [itex]dy= cos(\theta)d\theta[/itex], [itex]\theta[/itex] from [itex]\pi[/itex] to [itex]2\pi[/itex] (assuming you are integrating from (-1, 0) to (1, 0), you don't mention the orientation).
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  5. #5
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    Re: solving line integral by bounded area

    thanks
    Last edited by transgalactic; July 8th 2011 at 01:54 PM. Reason: hhm
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