What is the primary assumption of the trapezoidal rule and how is it applied to the integral integral02 2x2 dx with 4 subintervals?

The trapezoidal rule approximates the area under a curve by dividing the region into trapezoids. Therefore, the primary assumption is that the area under the function can be approximated by trapezoids.

The correct option is B.
B) The area under $f(x)$ can be approximated by trapezoids.

The integral is $\int_{0}^{2} 2x^2 dx$.
The interval is $[a, b] = [0, 2]$.
The number of subintervals is $n=4$.
The width of each subinterval is $\Delta x = \frac{b-a}{n} = \frac{2-0}{4}