 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/d/d3/a/solution

The function is nonnegative, measurable, and even. Direct integration gives

\int_{R} e^{- ∣ x ∣} d x = 2 \int_{0}^{\infty} e^{- x} d x = 2.

Thus it is integrable, with integral

2

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