Calculus

Find the volume or the solid generated by revolving around the region bounded by the graphs of the equations about line x=6. xy=6, y=2, y=6, and x=6

  1. 0
  2. 0
  3. 3
asked by Christina
  1. y=2 intersects xy=6 at (3,2)
    So we are rotating the region bounded by
    (3,2) to (6,2), then down to (6,1) and joining the curve back to (3,2)

    Vol = π∫(6-x)^2 dy from y = 1 to 2
    = π∫(36 - 12x + x^2) dy
    =π∫(36 - 12(6/y) + 36/y^2) dy from 1 to 2
    = π[ 36y - 72lny - 36/y ] from 1 to 2
    = π( (72 - 72ln2 - 18) - (36 - 72ln1 - 36) )
    = π(54 - 72ln2)
    = 18π(3 - 4ln2) or appr 12.86

    check my arithmetic

    1. 0
    2. 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6. y = 6 − x y = 0 y = 5 x = 0

    asked by ME on January 23, 2012
  2. Calculus 2

    Find the volume of the solid generated by revolving the region bounded by the graphs of the quations about the x-axis. Y=x^2+4 Y=-x^2+2x+8 X=0 X=3

    asked by Gabby on November 9, 2017
  3. Calculus Voulme

    find the volume of the solid generated by revolving the region r bounded by the graphs of the given equations about the y-axis. x^2+y^2=1 x=1 y=1

    asked by Laurie on July 19, 2012
  4. Calculus

    I would like to know if my answers are correct: Disclaimer: We are allowed to keep our answers in formula form 1. Use the washer method to find the volume of the solid that is generated by rotating the plane region bounded by

    asked by Daisy on January 16, 2017
  5. calculus

    find the volume of the solid generated by revolving the region bounded by the graphs of the equations y=2sqrtx, y=o, x=3 about the x-axis.

    asked by carlton on May 2, 2012
  6. Calculus

    "Find the volume of the solid generated by revolving the region bounded by the graphs of the given equations about the indicated lines: y = 2x^2 y = 0 x = 2 About the line y = 8"

    asked by Stuck on April 18, 2010
  7. Math (Calculus)

    Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. (Use Disc Method) y=3(2-x), y=0, x=0

    asked by Sherman on May 9, 2014
  8. Calculus

    Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y=ln x, y=0, x=1, x=3 Please show the steps in your work, thanks! :)

    asked by Pan on March 29, 2008
  9. Calculus

    Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y=ln x, y=0, x=1, x=3 Please show the steps in your work, thanks! :)

    asked by Sun on March 27, 2008
  10. Calculus

    Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = 0.5x^2, y = 2, and x = 0 about the line y = 2. A. 8pi/15 B. 32pi/15 C. 64pi/15 D. 4pi/15 E. 16pi/15

    asked by Anonymous on March 31, 2017

More Similar Questions