Answer is: option2

Solution:

We are given values of a function \( f(x) \) on the interval \([1, 12]\), and we are to approximate the integral

\[ \int_{1}^{12} f(x)\, dx \]

using the trapezoidal rule with subintervals:

\([1, 3], [3, 5], [5, 9], [9, 12]\)

The trapezoidal rule on each subinterval \([a, b]\) is:

\[ \frac{b - a}{2} \left[ f(a) + f(b) \right] \]

Let's compute the value on each interval:

Interval \([1, 3]\):

\[ \frac{3 - 1}{2} [f(1) + f(3)] = \frac{2}{2}[4 + 10] = 1 \cdot 14 = 14 \]

Interval \([3, 5]\):

\[ \frac{5 - 3}{2} [f(3) + f(5)] = \frac{2}{2}[10 + 14] = 1 \cdot 24 = 24 \]

Interval \([5, 9]\):

\[ \frac{9 - 5}{2} [f(5) + f(9)] = \frac{4}{2}[14 + 11] = 2 \cdot 25 = 50 \]

Interval \([9, 12]\):

\[ \frac{12 - 9}{2} [f(9) + f(12)] = \frac{3}{2}[11 + 7] = \frac{3}{2} \cdot 18 = 27 \]

Total Approximation:

\[ 14 + 24 + 50 + 27 = \boxed{115} \]

Option B