By using the trapezoidal rule with 6 ordinates, the approximate value of \( \int_{0}^{1} x^{2} e^{2 x} d x \) is 1.6951. What is the width of the subinterval? A \( \quad 0.1 \) B \( \quad 0.2 \) C \( \quad 0.3 \) D \( \quad 0.4 \)

To find the width of the subinterval using the trapezoidal rule with 6 ordinates over the interval from 0 to 1, we start by determining the total length of the interval, which is \( 1 - 0 = 1 \). Since we have 6 ordinates, we create 5 subintervals. The width \( h \) of each subinterval can be calculated by dividing the total length by the number of subintervals: \[ h = \frac{1}{6} = 0.1667 \] However, the question asks us to identify one of the options given. Let's check which of the options can be grouped together to approximately reach this width. While the exact answer of \( 0.1667 \) is not listed, the closest approximation within the options would likely be B \( \quad 0.2 \). Therefore, the answer among the options provided is: B \( \quad 0.2 \)