8.

Evaluate the integral 6te71" ) i+ (8e- 21) j + (2) k dt. C [ [ (Gte 7 ) it ( Be - 21) ; + 12) k dt=1 K 0 (Type exact answers.)Solve the following initial value problem for r as a function of t. dar Differential equation: = 2e'i - 5elj + 8e-k dt 2 Initial conditions: r(0) = 4i +j + 3k dr | = - 31 + 7j dt += 0 r(t) = it + KFind the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. r(t) = (3cost)j + (3sint)k, Osts 2 Find the curve's unit tangent vector. T(t) KFind the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. 41/2 r(t) = (-2t cost)i + ( - 2t sin t)j + 43/2k Osten 3 The curve's unit tangent vector is Di+ Di+ K (Type exact answers, using radicals as needed.)Find the point on the curve r(t)= (5 sin t}i + [ 5 cost)j12tk at a distance 131-: units along the curve from the point (0, 5:0) in the direction of increasing arc length. The point is ( i , ) (Type exact answers: usmg :r: as needed.)