csat-suneung 2019 Q17

csat-suneung · South-Korea · csat__math-humanities 4 marks Areas by integration
An increasing continuous function $f ( x )$ on the set of all real numbers satisfies the following conditions. (가) For all real numbers $x$, $f ( x ) = f ( x - 3 ) + 4$. (나) $\int _ { 0 } ^ { 6 } f ( x ) d x = 0$ What is the area enclosed by the graph of $y = f ( x )$, the $x$-axis, and the two lines $x = 6$ and $x = 9$? [4 points]
(1) 9
(2) 12
(3) 15
(4) 18
(5) 21
An increasing continuous function $f ( x )$ on the set of all real numbers satisfies the following conditions.\\
(가) For all real numbers $x$, $f ( x ) = f ( x - 3 ) + 4$.\\
(나) $\int _ { 0 } ^ { 6 } f ( x ) d x = 0$\\
What is the area enclosed by the graph of $y = f ( x )$, the $x$-axis, and the two lines $x = 6$ and $x = 9$? [4 points]\\
(1) 9\\
(2) 12\\
(3) 15\\
(4) 18\\
(5) 21