Volume of trig function around y-axisI have this question and it's the first kind of question I'm doing involving finding volume so I just would like some help solving this question:Find the volume created by revolving the curve y = sin ⁡ ( x ) x from x = π 3 to x = π. about the y-axis

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Volume of trig function around y-axisI have this question and it&#039;s the first kind of question I&#039;m doing involving finding volume so I just would like some help solving this question:Find the volume created by revolving the curve      y  =            sin      ⁡      (      x      )        x   from   x  =      π    3   to   x  =  π. about the y-axis

driogairea1 · Accepted Answer

Step 1Use the cylindrical shells formula:The volume of the solid obtained by revolving   {  (  x  ,  y  )      |    a  ≤  x  ≤  b  ,  0  ≤  y  ≤  f  (  x  )  } about the y-axis is:  V  =            ∫      a      b        2    π    x    f    (    x    )        d    x  Step 2Applying that formula here gives   V  =            ∫              π                  /                3                    π              2    π    x                            sin          ⁡          x                x                  d    x    =    2    π          ∫              π                  /                3                    π              sin    ⁡    x        d    x  .This gives you a simple integral to evaluate.

caritatsjq · Accepted Answer

Explanation:It will suffice to compute:  A  =      ∫          π              /            3        π    2  π  x  f  (  x  )         d    x where   f  (  x  )  =            sin      ⁡      x        x  . This is exactly the shell method.

Find the volume created by revolving the curve y=(sin(x))/x from x=pi/3 to x=pi.

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