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Math Help - Find the area of the region bounded by y and the x-axis

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    Find the area of the region bounded by y and the x-axis



    am I on the right track here?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Find the area of the region bounded by y and the x-axis

    Yes. I would write:

    A=\int_1^9 u^{\frac{1}{2}}\,du=\frac{2}{3}\left[u^{\frac{3}{2}} \right]_1^9=\frac{2}{3}(27-1)=\frac{52}{3}

    edit: Don't forget the differential in your definite integral and avoid using a rounded decimal approximation (at least if you have the same professor I did).
    Last edited by MarkFL; December 13th 2012 at 01:00 AM.
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    Re: Find the area of the region bounded by y and the x-axis

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    Re: Find the area of the region bounded by y and the x-axis

    Quote Originally Posted by MarkFL2 View Post
    Yes. I would write:

    A=\int_1^9 u^{\frac{1}{2}}\,du=\frac{2}{3}\left[u^{\frac{3}{2}} \right]_1^9=\frac{2}{3}(27-1)=\frac{52}{3}
    I see. So we assume u = (x+3) and go from there. Looks more professional to me. Thanks! On thing I'm not sure about though is, how did you get the 9 and 1?
    EDIT: Oh nevermind. I get it now.

    Quote Originally Posted by a tutor View Post
    That's fine. You can check this sort of thing here integral (-2,6) (x+3)^(1/2) dx - Wolfram|Alpha
    Oh that tool is amazing! So I take it the graph shown there is the sketch of the region.
    Last edited by theunforgiven; December 13th 2012 at 01:04 AM.
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