 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2016-resit/2/ii/solution

For

- 1 \leq y \leq 0

, a horizontal slice runs from

x = - 1

to the line

x = y

. For

0 \leq y \leq 1

, it runs from

x = - 1

to the negative branch

x = - y

of the parabola. Thus the reversed iterated integral is

\int_{- 1}^{0} \int_{- 1}^{y} y d x d y + \int_{0}^{1} \int_{- 1}^{- y} y d x d y .

The positive branch

x = y

is outside the original integration region.

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