Green’s theorem gives the relationship between a line integral around a simple closed curve C2. Consider the line integral jg F – dr, where the vector ?eld 0F = 333(cosa: + y)i + 394(sin2 y + x) j and C is the triangle in the myplane with corners at (0,0), (2, 0) and (0, 2), taken anticlockwise.(a) Use Greens theorem to express the line integral in terms of a double integralover the region R enclosed by C. (b) Calculate the double integral using a repeated integral with respect to x ?rstand y second. (0) Now reverse the order of integration and evaluate the double integral using arepeated integral with respect to y ?rst and a: second.
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