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
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
Evaluating: s(t) = 7t^2