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

Find the length of the arc of y=x2/2- x/4 from x=1 to x=2.

  1. 2/2 + 3/2 1.847
  2. 2/4 + 3/2 1.673
  3. 3/2 - 2/4 1.327
  4. 2 + 3/2 2.193

Answer

B. 2/4 + 3/2 1.673

Solution

y'=x-1/4x, so 1+(y')2=≤ft(x+1/4x )2. L= 12≤ft(x+1/4x )dx=≤ft[x2/2+ x/4 ]12= 32+ 2/4.

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