The graph of a function is shown as a blue curve. This visualization demonstrates how to use a midpoint approximation to estimate the area under the curve in the interval \([-5, 1]\) with 6 rectangles.### Description- **Endpoints Adjustment**: Orange points are present on the horizontal axis that can be moved to adjust the interval endpoints.- **Rectangle Control**: A vertical slider on the right side of the graphing window, indicated by a blue movable point, changes the number of rectangles used for the approximation.- **Rectangle Characteristics**: - The width of each rectangle is marked with \(\Delta x\). - Black movable points atop each rectangle allow adjustment of their height.### Current Graph State- The interval is from \(a = -3\) to \(b = 5\).- The current number of rectangles is \(n = 4\).- The width of each rectangle, \(\Delta x\), is 2.- Green rectangular areas depict the applied midpoint approximation under the blue curve, adjusted by the black movable points.The interactive visualization allows for dynamic experimentation with the rectangle count and interval settings to explore how these changes affect the area approximation.

The given graph is drawn as follows.We need to find the midpoint approximation of the area under curve on the interval using intervals.We know that the area under curve of a function on the interval with sub interval is approximated using midpoint method as follows., where .The given interval is and number of intervals are .Therefore the size of sub interval..Therefore the endpoints of sub intervals are:.Let the given graph is correspond to the function .From the graph, observed that:Therefore the area under the curve on the interval with sub interval using mid point approximation is calculated as follows.Hence tha approximated area under curve uing mid point approximation is square unit.