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Math Help - Find area (image included)

  1. #1
    Junior Member
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    Find area (image included)

    Find area (image included)-6_1_13.gif

    I've only learned the area between two curves and integration along the y-axis...I'm really confused on how to start this one. Do I find the slope of the lines and go from there? Any help would be greatly appreciated
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  2. #2
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    e^(i*pi)'s Avatar
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    I would take the whole area and subtract the non shaded parts

    \displaystyle \int^{\pi /2}_0 \cos(x) \,dx - \left( \int^{\pi /6}_0 \cos(x) \,dx + \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{\pi}{2}\right)

    in case you're wondering the last term is the area of a triangle

    Don't quote me on it though, someone may have a better answer!
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  3. #3
    MHF Contributor
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    You could also calculate

    \displaystyle\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}c  osxdx+\frac{1}{2}\frac{\pi}{6}\frac{\sqrt{3}}{2}-\frac{1}{2}\frac{1}{2}\frac{\pi}{3}

    In other words, the area under the curve from \frac{\pi}{6}\rightarrow\frac{\pi}{3}

    then add in the area of the upper triangle and subtract the lower one..

    @ e^(i*pi)

    the last part isn't a triangle (the curve is cosx there).
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