# Consider the line integral jg F – dr, where the vector eld 0 F = 333(cosa: + y)i + 394(sin2 y + x) j and C is the triangle in the myplane with…

Green’s theorem gives the relationship between a line integral around a simple closed curve C

2. Consider the line integral jg F – dr, where the vector ﬁeld 0F = 333(cosa: + y)i + 394(sin2 y + x) j and C is the triangle in the my—plane with corners at (0,0), (2, 0) and (0, 2), taken anticlockwise.(a) Use Green’s 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 ﬁrstand y second. (0) Now reverse the order of integration and evaluate the double integral using arepeated integral with respect to y ﬁrst and a: second.