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

The region under y=e-x for x≥0 is revolved about the x-axis. Find the volume of the resulting solid.

  1. π 3.14
  2. π/4 0.79
  3. π/2 1.57
  4. 2 π 6.28

Answer

C. π/2 1.57

Solution

V=π 0∞ e-2xdx=π≤ft[- e-2x2 ]0∞=π/2.

More Applications: Volume, Arc Length, Surface Area questions

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

All Applications: Volume, Arc Length, Surface Area questions