312 Let C be the parameterized curve given by rt t t2 t for

3.12 Let C be the parameterized curve given by r(t) = [t, t^2, t] for 1< = t < = 2.

(a) Set up (but do not evaluate) the definite integral that evaluates the line integral IntC xyz ds.

Solution

. so we get, Since t = 0 <==> (x, y, z) = (1, 0, 0), we let t = 0 in r\' to find the direction vector for the tangent line. r\'(0) = <1, 1, 1>. So, the equation of the tangent line is l(t) = <1, 0, 0> + t<1, 1, 1> = <1 + t, t, t>. Parametrically, this is given as x = 1 + t y = t z = t. answer