csat-suneung 2014 Q29

csat-suneung · South-Korea · csat__math-A 4 marks Integration by Substitution Substitution to Evaluate a Definite Integral (Numerical Answer)
The function $f ( x ) = 3 x ^ { 2 } - a x$ satisfies
$$\lim _ { n \rightarrow \infty } \frac { 1 } { n } \sum _ { k = 1 } ^ { n } f \left( \frac { 3 k } { n } \right) = f ( 1 )$$
Find the value of the constant $a$. [4 points]
The function $f ( x ) = 3 x ^ { 2 } - a x$ satisfies

$$\lim _ { n \rightarrow \infty } \frac { 1 } { n } \sum _ { k = 1 } ^ { n } f \left( \frac { 3 k } { n } \right) = f ( 1 )$$

Find the value of the constant $a$. [4 points]