Calculus arc length help
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Calculus arc length help

[From: ] [author: ] [Date: 11-08-31] [Hit: ]
k are i hat,i know i need R.then the next step is R(t) . R(t) which is 196t^2(.how do i solve this integral-s(t) = ∫ {0, t} √(196x^2) dx = ∫ {0,......
the following R(t) for 0<= t <= infinity defines a space curve. find the arc length s as a function of the parameter t, namely s(t) if t = 0 is taken to correspond to s = 0.

i - 7t^2 j +3k (i, j, k are i hat, j hat and k hat)

i know i need R'.
R' = 14t j

then the next step is R'(t) . R'(t) which is 196t^2 (. is the vector operation dot)

im stuck at the integral which is s(t) = integral (0 to t) sqrt(196t^2) dt
how do i solve this integral

s(t) = ∫ {0, t} √(196x^2) dx = ∫ {0, t} 14x dx = 7x^2

Evaluating: s(t) = 7t^2
keywords: arc,help,Calculus,length,Calculus arc length help
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