정적분 값 정수 범위

구간 $0 \leq x \leq 2$에서 $0 \leq \sin x \leq 1$이므로 $\displaystyle \int _{0} ^{2} \sqrt{27} dx < \int _{0} ^{2} \sqrt{27 + 2 \sin x} dx < \int _{0} ^{2} \sqrt{29} dx$ $\displaystyle \sqrt{27} x ] _{0} ^{2} < \int _{0} ^{2} \sqrt{27 + 2 \sin x} dx < \sqrt{29} x ] _{0} ^{2}$ $\displaystyle \sqrt{108} < \int _{0} ^{2} \sqrt{27 + 2 \sin x} dx < \sqrt{116}$ $\displaystyle 10 < \sqrt{108} < \int _{0} ^{2} \sqrt{27 + 2 \sin x} dx < \sqrt{116} < 11$ $\therefore n = 10$