Calculus

posted by .

The region between the graphs of x=y^2 and x=4y is rotated around the line y=4.
The volume of the resulting solid is?

  • Calculus -

    I assume you made a sketch.
    You should have the two graphs intersecting at (0.0) and (16,4)

    So we will washer discs with outer ratius of 4 - x/4 and inner radius of 4 - √x

    area of washer disc = π(4-x/4)^2 = π(4-√x)^2
    = π(16 - 2x + x^2/4 - (16 - 8√x + x)
    = π( -3x + x^2 + 8x^(1/2)

    volume = π∫(-3x + x^2 + 8x^(1/2) dx from 0 to 16
    = π [ (-3/2)x^2 + (1/3)x^3 + (16/3)x^(3/2) ] from 0 to 16

    = π(-384 + 4096/3 + 1024/3 - 0]
    = π(3968/3)

    check my arithmetic

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    The region between the graphs of y=x^2 and y=2x is rotated around the line x=2. The volume of the resulting solid is ____. Please help. I've tried this problem so many times but i keep getting it wrong. I thought the outer radius would …
  2. Calculus

    This is a tough one :( The region between the graphs of x=y^2 and x=6y is rotated around the line y=6. Find the volume of the resulting solid please... i am unable to get the correct answer :(
  3. Calculus

    The region between the graphs of x=y^2 and x=6y is rotated around the line y=6. Find the volume of the resulting solid please... i am unable to get the correct answer :(
  4. Calculus

    The region between the graphs of x=y^2 and x=4y is rotated around the line y=4. The volume of the resulting solid is how so i solve?
  5. CALCULUS:)

    The region between the graphs of x=y^2 and x=6y is rotated around the line y=6. The volume of the resulting solid is ____?
  6. math

    The region between the graphs of x=y2 and x=5y is rotated around the line y=5. Find the volume of the resulting solid.
  7. math

    The region between the graphs of x=y2 and x=5y is rotated around the line y=5. Find the volume of the resulting solid.
  8. math

    The region between the graphs of x=y2 and x=5y is rotated around the line y=5. Find the volume of the resulting solid.
  9. Calculus

    The region between the graphs of x=y^(2)and x=2y is rotated around the line y=2. The volume of the resulting solid is... I've tried this five times and no luck. Please help. I think my a=o and b=2. I would appreciate the help.
  10. Cal 2

    The region between the graphs of y=x^2 and y=3x is rotated around the line x=3. The volume of the resulting solid is

More Similar Questions