csat-suneung· South-Korea· csat__math-science3 marks
A polynomial function $f ( x )$ satisfies $$\int _ { 1 } ^ { x } f ( t ) d t = x ^ { 3 } - 2 a x ^ { 2 } + a x$$ for all real numbers $x$. Find the value of $f ( 3 )$. (Here, $a$ is a constant.) [3 points]
A polynomial function $f ( x )$ satisfies
$$\int _ { 1 } ^ { x } f ( t ) d t = x ^ { 3 } - 2 a x ^ { 2 } + a x$$
for all real numbers $x$. Find the value of $f ( 3 )$. (Here, $a$ is a constant.) [3 points]