Three Typical Questions on Green's Theorem

Green's Theorem is a mainstay of undergraduate courses, linking vector fields, curl, line integrals and double integrals (amongst others). In our experience there are three principal types of 'Green's Theorem' questions on exams, testing firstly how to find the area of a simple closed curve such as an ellipse; secondly how to solve a very complex line integral by spotting that Green's Theorem converts it to a fairly simple double integral; and thirdly testing ability to do an integral 'both ways' (line and double) and confirming therefore that Green's Theorem holds.
In this video we discuss all three of these question types by reference to actual exam questions that we have found.
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