Engineering Board Exam Reviewer · Applications: Area Between Curves · medium

Find the area under one arch of the cycloid x=3(t- t), y=3(1- t).

  1. 9 π 28.27
  2. 27 π 84.82
  3. 18 π 56.55
  4. 3 π 9.42

Answer

B. 27 π 84.82

Solution

A= 02πy,dx/dt,dt= 02π9(1- t)2,dt=9≤ft(2π+π )=27π.

More Applications: Area Between Curves questions

  1. Find the area of the region bounded by the parabolas y=x2 and y=8-x2.
  2. Find the area bounded by y=x2 and y=4.
  3. Find the area under the curve y=x3 from x=0 to x=2.
  4. Find the area enclosed between y=x and y=x2 from x=0 to x=1.
  5. Find the area between the curve y=6x-x2 and the x-axis.
  6. Find the area bounded by y=sqrt(x), the x-axis, and x=4.
  7. Find the area between y=x2 and y=2x from x=0 to x=2.
  8. Find the area enclosed by the astroid x=2 3t, y=2 3t.
  9. Find the total area enclosed by the lemniscate r2=16 2 .
  10. Find the area of the region that lies inside the circle r=3 and outside the cardioid r=1+ .

All Applications: Area Between Curves questions