1. i 성분: \displaystyle \int_{0}^{\frac{\pi}{4}} \sec^2tdt = \left[ \tan t \right]_{0}^{\frac{\pi}{4}} = 1 - 0 = 1

2. j 성분: \displaystyle \int_{0}^{\frac{\pi}{4}} \tan tdt = \left[ -\ln|\cos t| \right]_{0}^{\frac{\pi}{4}} = -\ln(\dfrac{\sqrt{2}}{2}) - (-\ln 1) = -\ln(\dfrac{\sqrt{2}}{2}) = \ln(\dfrac{2}{\sqrt{2}}) = \ln(\sqrt{2})

3. k 성분: \displaystyle \int_{0}^{\frac{\pi}{4}} 2tdt = \left[ t^2 \right]_{0}^{\frac{\pi}{4}} = \dfrac{\pi^2}{16}

결과는 \displaystyle \langle 1, \ln(\sqrt{2}), \dfrac{\pi^2}{16} \rangle이다.