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Math Help - Area between parametric curve

  1. #1
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    Area between parametric curve

    Having trouble finding the area between this parametric curve and the y axis can someone go over my work please. Thanks in advance!

    x= t^2-5t, y= t^\frac{1}{2}

    Interescts the y-axis when x=0 or when t=0,5

    So, A= \int_0^5 \! x(t)*y' \, dt
    = \int_0^5 \! (t^2-5t)(\frac{1}{2t^\frac{1}{2}}) \, dt
    = \frac{1}{2}\int_0^5 \! t^\frac{3}{2}-5t^\frac{1}{2} \, dt
    = \frac{1}{2}[\frac{2}{5}t^\frac{5}{2}-5*\frac{2}{3}t^\frac{3}{2} \,\bigg|_0^5
    = \frac{1}{5}t^\frac{5}{2}-\frac{5}{3}t^\frac{3}{2} \,\bigg|_0^5
    = 1-(\frac{25}{3})^\frac{3}{2}
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  2. #2
    MHF Contributor Calculus26's Avatar
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    See the attachment below

    Note x -s negative over the range so use - x(t) y' (t)

    that aside that you are correct to



    but your evaluation is incorrect-- see also attachment
    Attached Thumbnails Attached Thumbnails Area between parametric curve-area.jpg  
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