 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/3/a/solution

Since the derivative of

ln cos x

- tan x

on this interval,

\int_{0}^{π /4} tan x d x = [- ln cos x]_{0}^{π /4} = - ln \frac{1}{2} = \frac{1}{2} ln 2 .

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