csat-suneung 2024 Q12

csat-suneung · South-Korea · csat__math 4 marks Areas by integration

For the function $f(x) = \frac{1}{9}x(x-6)(x-9)$ and a real number $t$ with $0 < t < 6$, the function $g(x)$ is defined as $$g(x) = \begin{cases} f(x) & (x < t) \\ -(x-t) + f(t) & (x \geq t) \end{cases}$$ Find the maximum area of the region enclosed by the graph of $y = g(x)$ and the $x$-axis. [4 points]
(1) $\frac{125}{4}$
(2) $\frac{127}{4}$
(3) $\frac{129}{4}$
(4) $\frac{131}{4}$
(5) $\frac{133}{4}$

For the function $f(x) = \frac{1}{9}x(x-6)(x-9)$ and a real number $t$ with $0 < t < 6$, the function $g(x)$ is defined as
$$g(x) = \begin{cases} f(x) & (x < t) \\ -(x-t) + f(t) & (x \geq t) \end{cases}$$
Find the maximum area of the region enclosed by the graph of $y = g(x)$ and the $x$-axis. [4 points]\\
(1) $\frac{125}{4}$\\
(2) $\frac{127}{4}$\\
(3) $\frac{129}{4}$\\
(4) $\frac{131}{4}$\\
(5) $\frac{133}{4}$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q23_calculus Q23_geometry Q24 Q24_calculus Q24_geometry Q25 Q25_calculus Q25_geometry Q26 Q26_calculus Q26_geometry Q27 Q27_calculus Q27_geometry Q28 Q28_calculus Q28_geometry Q29 Q29_geometry Q30 Q30_geometry