csat-suneung 2015 Q20

csat-suneung · South-Korea · csat__math-A 4 marks Indefinite & Definite Integrals Piecewise/Periodic Function Integration
The function $f ( x )$ satisfies $f ( x + 3 ) = f ( x )$ for all real numbers $x$, and $$f ( x ) = \begin{cases} x & ( 0 \leq x < 1 ) \\ 1 & ( 1 \leq x < 2 ) \\ - x + 3 & ( 2 \leq x < 3 ) \end{cases}$$ If $\int _ { - a } ^ { a } f ( x ) d x = 13$, what is the value of the constant $a$? [4 points]
(1) 10
(2) 12
(3) 14
(4) 16
(5) 18
The function $f ( x )$ satisfies $f ( x + 3 ) = f ( x )$ for all real numbers $x$, and
$$f ( x ) = \begin{cases} x & ( 0 \leq x < 1 ) \\ 1 & ( 1 \leq x < 2 ) \\ - x + 3 & ( 2 \leq x < 3 ) \end{cases}$$
If $\int _ { - a } ^ { a } f ( x ) d x = 13$, what is the value of the constant $a$? [4 points]\\
(1) 10\\
(2) 12\\
(3) 14\\
(4) 16\\
(5) 18