About finding the rotational volumeA closed area of y-axis, y = π , y = x + s i n ( x ) is rotated on line y = x. Find the volume of it.So, I think I have to do an integral looks like this. V = ∫ 0 2 π π r 2 d t, where r is the radius of disk and t is a variable on line y = x.How should I set up the integral and change the variables?

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About finding the rotational volumeA closed area of y-axis,   y  =  π  ,  y  =  x  +  s  i  n  (  x  ) is rotated on line   y  =  x. Find the volume of it.So, I think I have to do an integral looks like this.  V  =      ∫          0                      2            π        π      r    2    d  t, where r is the radius of disk and t is a variable on line   y  =  x.How should I set up the integral and change the variables?

trollbabyfeetwa · Accepted Answer

Explanation:You need to show that the distance from a point of the curve   y  =  f  (  x  ) and the line   y  =  x is   r  (  x      )    2    =  [  f  (  x  )  −  x      ]    2        /    2. In this case,   f  (  x  )  =  x  +  sin  ⁡      x  . Then the volume is   π      ∫    0          π        d  x    r  (  x      )    2

A closed area of y-axis, y=pi, y=x+sin(x) is rotated on line y=x. Find the volume of it.

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