We are given:
$\sum_{i=1}^{10} X_i - 10A = 2 \implies \sum_{i=1}^{10} X_i = 10A + 2$.
$\sum_{i=1}^{10} X_i - 10B = 40 \implies \sum_{i=1}^{10} X_i = 10B + 40$.
Equating both expressions for $\sum_{i=1}^{10} X_i$, we get:
$10A + 2 = 10B + 40 \implies 10A - 10B = 38 \implies A - B = 3.8$.
Since A and B are integers, $A = 4$ and $B = 2$.
Thus, $B = 2$.
If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to: