Volume: The Disk Method AP Calculus ABFinding the Volume of a Solid - Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis y = e − x , y = 0 , x = 0 , y = 1Why would the upper limit of integration be 1?

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Volume: The Disk Method AP Calculus ABFinding the Volume of a Solid - Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis  y  =      e          −      x        ,     y  =  0  ,     x  =  0  ,     y  =  1Why would the upper limit of integration be 1?

Andres Barrett · Accepted Answer

Step 1It should be   x  =  1, not   y  =  1.Shell Method:       ∫                  1        e                    1        −  2  π  y  l  n  y  d  y  +      ∫          0                      1        e              2  π  y  (  1  )  d  yStep 2Washer Method:       ∫          0              1        π  (      e          −      x            )          2        d  x

Roderick Bradley · Accepted Answer

Explanation:  x  =  1, not   y  =  1.At least this is consistent with the given answer, since       ∫    0    1    π      e          −      2      x          d  x  =      π    2    (  1  −      e          −      2        )  ≈  1.358.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis y=e^{-x}, y=0, x=0, y=1.

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