Sketch the region bounded by the curves: y=ln⁡x,y=0y=ln⁡x,y=0 and x=ex=e, then find, the area of...



Answered question


Sketch the region bounded by the curves: y=lnx,y=0y=lnx,y=0 and x=ex=e, then find, the area of this region, and find the volume of the solid generated by revolving this area about the line x=2?x=2?

Answer & Explanation



Skilled2021-01-29Added 88 answers

The sketch is easily obtainable through a graphing software/website, it’s also very easy to sketch it from basic principles. As for the area of the figure,
You should notice that we are essentially finding the area of the curve ln(x) from 11 to e.
As for the solid of revolution, we have to use the washer method, which has a ring of constant outer radius (e+2)(e+2) and a ring of inner radius ey+2
Therefore, we can just compute:

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