Engineering Board Exam Reviewer · Applications: Volume, Arc Length, Surface Area · medium

The region bounded by y=x and y=x2 is revolved about the x-axis. Find the volume of the solid generated.

  1. 2 π/15 0.42
  2. π/15 0.21
  3. 4 π/15 0.84
  4. 2 π/5 1.26

Answer

A. 2 π/15 0.42

Solution

Washers: V=π 01≤ft(x2-x4 )dx=π≤ft( 13- 15 )=2π/15.

More Applications: Volume, Arc Length, Surface Area questions

  1. The region bounded by y=x2, x=0, x=2, and the x-axis is revolved about the x-axis. Find the volume generated.
  2. The region bounded by y=sqrt(x), x=0, and x=4 is revolved about the x-axis. Find the volume generated.
  3. The region bounded by y=x, x=0, and y=3 is revolved about the y-axis. Find the volume generated.
  4. Find the length of the arc of the curve y=x3/2 from x=0 to x=4.
  5. Find the surface area generated by revolving the line y=x from x=0 to x=3 about the x-axis.
  6. Find the length of the arc of y= 23x3/2 from x=0 to x=3.
  7. The circle (x-5)2+y2=4 is revolved about the y-axis to form a torus. Find its volume.
  8. Find the area of the surface generated by revolving y=2sqrt(x), 0≤ x≤3, about the x-axis.
  9. Find the area of the surface generated by revolving y=x3, 0≤ x≤1, about the x-axis.
  10. Find the length of the catenary y=5 x5 from x=0 to x=5.

All Applications: Volume, Arc Length, Surface Area questions