Finding volume of a solid about a vertical lineHow can I calculate the volume of the solid generated by rotating the region bounded by y = x 2 − 6 x + 10and y = − x 2 + 4 x + 2.About the line x = 4

Question

Finding volume of a solid about a vertical lineHow can I calculate the volume of the solid generated by rotating the region bounded by  y  =      x    2    −  6  x  +  10and   y  =  −      x    2    +  4  x  +  2.About the line   x  =  4

Tristan Pittman · Accepted Answer

Step 1Use cylindrical shells.Your representative rectangle would be vertical, and its width is dx and its height is  −      x    2    +  4  x  +  2  −  (      x    2    −  6  x  +  10  )  =  −  2      x    2    +  10  x  −  8Step 2Now, construct your integral:  2  π      ∫          1        4    p  (  x  )  h  (  x  )  d  x  p  (  x  )  =  4  −  x since you&#039;re rotating around the line   x  =  4.  2  π      ∫          1        4    (  4  −  x  )  ∗  (  −  2      x    2    +  10  x  −  8  )  d  x  =            27      π        2  comment if you need more help.