절댓값 정적분

[출제의도] 정적분의 값을 구할 수 있는가? $\displaystyle \int _{1} ^{4} {} \left( x + \left| x - 3 \right| \right) dx$ $\displaystyle = \int _{1} ^{3} {} \left( x + \left| x - 3 \right| \right) dx + \int _{3} ^{4} {} \left( x + \left| x - 3 \right| \right) dx$ $\displaystyle = \int _{1} ^{3} {} \left( x - \left( x - 3 \right) \right) dx + \int _{3} ^{4} {} \left( x + ( x - 3 \right) ) dx$ $\displaystyle = \int _{1} ^{3} {3 dx} + \int _{3} ^{4} {( 2 x - 3 ) dx}$ $= \left[ 3 x \right] _{1} ^{3} + \left[ x ^{2} - 3 x \right] _{3} ^{4}$ $= ( 9 - 3 ) + \left\{ ( 16 - 12 ) - ( 9 - 9 ) \right\}$ $= 10$