02-12-2016
Mathematics

Answered

Find the length of the curve

x=1−t,y=t−5,z=2t−2,

for 1≤t≤3

Verified Answer :

wizard123 wizard123

02-12-2016

To find length of curve use:
\(\int\limits^a_b {|r'(t)|} \, dt\)
where r(t) is vector equation:
\(r(t) = (1,-5,-2) + (-1,1,2)t\)
\(r'(t) = (-1,1,2)\)
Magnitude of vector r'(t) is then:
\(\sqrt{(-1)^2 +1^2 +2^2} =\sqrt{6}\)
Now evaluate integral
\(\int\limits^3_1 {\sqrt{6}} \, dt = \sqrt{6} (3-1) = 2 \sqrt{6}\)

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