Question

Sketch the graph of some function f on [2, 5] for which SIMP(6) (i.e., with $\frac{n}{2}=3$parabola-topped rectangles) is an under-approximation for${\int }_a^{b}f\left(x\right)dx$

Short answer

Integral is${\int }_a^{b}f\left(x\right)dx$

Step-by-step solution

Step 1. Given information

Integral is${\int }_a^{b}f\left(x\right)dx$

Step 2. Explanation

Each graph interval is approximated as a parabola going through the points of function at the initial, midway, and end point of intervals using Simpson's approach. The goal is to draw a graph that is an under-approximation in Simpson's approximation using three divisions in the interval [2,5].