4. (7 p) Consider the vector field = e + [xe + In(z)] } + ....

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4. (7 p) Consider the vector field = e + [xe + In(z)] } + . (i) Is there a potential function associated with G? (ii) If there is, then find it. (iii) If applicable, use the Fundamental Theorem for Line Integrals to evaluate .dr where C is any curve joining the points A(0, 1, 1) and B(1,0,2). 5. (10 p) Evaluate the following integrals (hint: Fubini's Theorem): 2 (a)x cos(y) dy dr (b) ey/* dx dy y/2 4. (7 p) Consider the vector field = e + [xe + In(z)] } + . (i) Is there a potential function associated with G? (ii) If there is, then find it. (iii) If applicable, use the Fundamental Theorem for Line Integrals to evaluate .dr where C is any curve joining the points A(0, 1, 1) and B(1,0,2). 5. (10 p) Evaluate the following integrals (hint: Fubini's Theorem): 2 (a)x cos(y) dy dr (b) ey/* dx dy y/2