Ask questions and get helpful responses.

Calculus

Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = −3.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. The region is a triangular patch with vertices at (1,0), (1,1), and (1,e)
    So the volume is a stack of washers of thickness dx:
    v = ∫[1,e] π(R^2-r^2) dx
    where R=(1+3) and r=(lnx+3)
    v = ∫[1,e] π(4^2-(lnx+3)^2) dx

    Or, you can set it up as a stack of nested shells of thickness dy
    v = ∫[0,1] 2πrh dy
    where r=y+3 and h=x-1=e^y-1
    v = ∫[0,1] 2π(y+3)(e^y-1) dy

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Still need help? You can ask a new question.