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Math Help - Area Between Curves

  1. #1
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    Area Between Curves

    Let R be the region bounded by the graph of y =x ex cos(x), the origin and the line x = 2.

    Sketch the graph of R. Show the scale.
    Find the area of region R.

    So far, I've tried to sketch the region and this is all I have. I'm not even sure if it's right.
    Look at the link below, please.

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  2. #2
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    This is your function? \displaystyle y = xe^x\cos x

    Does it intersect the x-axis on the interval \displaystyle (0,2) ?
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  3. #3
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    Yes.
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  4. #4
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    Ok, now solve

     \displaystyle \int_{0}^{\frac{\pi}{2}}xe^x\cos x  ~dx + \left|\int_{\frac{\pi}{2}}^{2}xe^x\cos x  ~dx\right|
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