(a) Consider the vector field F(x, y) = (sin y+ex, x cos y). Explain concisely why...

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(a) Consider the vector field F(x, y) = (sin y+ex, x cos y). Explain concisely why F with domain R2 is conservative, and find its potential function f. (b) Let C be any smooth curve starting at A = (0, 0) and ending at B = (1,0). Using the Fundamental Theorem for Line Integrals, compute F.dr. C (a) Consider the vector field F(x, y) = (sin y+ex, x cos y). Explain concisely why F with domain R2 is conservative, and find its potential function f. (b) Let C be any smooth curve starting at A = (0, 0) and ending at B = (1,0). Using the Fundamental Theorem for Line Integrals, compute F.dr. C