$25 \cdot 30$ Let the area bounded by the $x$-axis, the line $x=8$, and the curve $f=\{(x, y) \mid y=x$, where $0 \leqslant x \leqslant 5, y=2 x-5$ where $5 \leqslant x \leqslant 8\}$ be $k, k$ equals
(A) 21.5 .
(B) 36.4 .
(C) 36.5 .
(D) 44 .
(E) Less than 44 but close to 44 .
(20th American High School Mathematics Examination, 1969)
[Solution] It is easy to draw the graph of the curve $f$ as shown on the right.
$$
\begin{aligned}
\therefore \quad k & =S_{\triangle A O D}+S_{\text {trapezoid } A B C D} \\
& =\frac{1}{2} \cdot 5 \cdot 5+\frac{1}{2} \cdot 3 \cdot(11+5) \\
& =36.5 .
\end{aligned}
$$

Therefore, the correct choice is $(C)$.