2. Consider the vector field F(r, y) = [x, y). (a) Show that F is path independent by showing that F is a gradient, ie. find a function f(z, y) such that F = Vf. (b) Compute algebraically the line integrals over the three paths A, B,C as shown in the figure below, from (0,0) to (1, 1). Check that the value of the integrals are all equal. To be more precise, A is a line segment, B is part of the graph f(x) = 1, and C consists of two line segments meeting at a right angle. (1, 1) A C B (c) Use your answer to part (a) and the FTC for line integrals to evaluate F - dr, F - dř, F- di

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