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

Find the length of the curve y= ( x) from x=0 to x= π4.

  1. 2 0.693
  2. -1 + sqrt(2) 0.414
  3. ≤ft(1 + sqrt(2) ) 0.881
  4. π/4 0.785

Answer

C. ≤ft(1 + sqrt(2) ) 0.881

Solution

y'= x, so sqrt(1+y'2)= x. L= 0π/4 x,dx= | x+ x| |0π/4= ≤ft( 2+1 ).

More Applications: Volume, Arc Length, Surface Area questions

  1. Find the length of the arc of y=x2/2- x/4 from x=1 to x=2.
  2. The base of a solid is the region between y=x2 and y=8-x2. Cross sections perpendicular to the x-axis are semicircles whose diameters lie…
  3. The base of a solid is the circle x2+y2=16. Cross sections perpendicular to the x-axis are squares. Find the volume of the solid.
  4. The region bounded by y=sqrt(x), the x-axis, and x=4 is revolved about the line y=2. Find the volume generated.
  5. The region bounded by y=x and y=x2 is revolved about the line x=2. Find the volume generated.
  6. The ellipse x2/9+y2/4=1 is revolved about the x-axis. Find the volume of the ellipsoid.
  7. The region bounded by y=x3, the y-axis, and y=8 is revolved about the y-axis. Find the volume generated.
  8. The region under y=e-x for x≥0 is revolved about the x-axis. Find the volume of the resulting solid.
  9. The region bounded by y=x and y=x2 is revolved about the x-axis. Find the volume of the solid generated.
  10. The region bounded by y=x2, x=0, x=2, and the x-axis is revolved about the x-axis. Find the volume generated.

All Applications: Volume, Arc Length, Surface Area questions