Question 1

1/6 Evaluate the integral [(3+6 cos t) i + (4 sin t) j+ (2 sec t) k] dt. - 1/6 The result is i+ K. (Type exact answers, using x and radicals as needed.)\fSolve the initial value problem for r as a vector function of t. dr Differential equation: dt = - 5ti - 5t j- 3t k Initial condition: r(0) = 4i + 3j + 4k it +\fSolve the following initial value problem for r as a function of t. Differential equation: 2 = 3eli - 5e-j + 42 k dt Initial conditions: (0) = 6i + j + 2k dr dt = - 2i + 7j It= 0 III r(t) = + k