Find the line integral of \(F = 2\sqrt{x}i - 3xj + \sqrt{y}k\), from \((0, 0, 0)\) to \((1, 1, 1)\) over each of the following paths
a. The straight-line path \(C_1: r(t) = ti + tj + tk\), \(0 \le t \le 1\)
b. The curved path \(C_2: r(t) = ti + t^2j + t^3k\), \(0 \le t \le 1\)
c. The path \(C_3 \cup C_4\) consisting of the line segment from \((0, 0, 0)\) to \((1, 1, 0)\) followed by the segment from \((1, 1, 0)\) to \((1, 1, 1)\)