부분적분 계산

[출제의도] 부분적분법 이해하기 부분적분법에 의하여 $f \left( x \right) = x + 1$, $g' \left( x \right) = \cos x$라 하면 $f' \left( x \right) = 1$, $g \left( x \right) = \sin x$이므로 $\displaystyle \int _{0} ^{\frac{\pi}{2}} {\left( x + 1 \right) \cos x} dx$ $\displaystyle = \left[ \left( x + 1 \right) \sin x _{{}_{}} ^{{}^{}} \right] _{0} ^{\frac{\pi}{2}} - \int _{0} ^{\frac{\pi}{2}} {\sin x} dx$ $\displaystyle = \left( \frac{\pi}{2} + 1 \right) - \left[ - \cos x _{{}_{}} ^{{}^{}} \right] _{0} ^{\frac{\pi}{2}}$ $\displaystyle = \frac{\pi}{2}$