Understanding shell height (finding volume)- Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the region under curve y = x from 0 to 1.Shell radius = yShell height = 1 − y 2 V = 2 π ∫ 0 1 y ( 1 − y 2 ) d yI didn't understand the shell height, why it is 1 − y 2 ? Why not y 2 ? I think, shell height should be y 2 . Can you explain?

Question

Understanding shell height (finding volume)- Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the region under curve   y  =      x   from 0 to 1.Shell radius   =  yShell height   =  1  −      y          2        V  =  2  π      ∫          0              1        y      (    1    −          y              2              )    d  yI didn&#039;t understand the shell height, why it is   1  −      y    2  ? Why not       y    2  ? I think, shell height should be       y    2  . Can you explain?

aguraire1jm · Accepted Answer

Explanation:The region is bounded on the left by   y  =      x  , which can be rewritten as   x  =      y    2  .The region is also bounded on the right by   x  =  1Hence   1  −      y    2

Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the region under curve y=sqrt{x} from 0 to 1.

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