Calculating the area under a curve is a standard problem in numerical methods. What you will develop is an app that calculates and displays the area under a range of curves.

Figure 1: Area under the curve of y = x² over the range 1 to 2, with 1 trapezoid.

The area can be calculated by drawing one or more polygons (trapezoids) that approximate the curve. We start by drawing a trapezoid that encompasses our curve between the given limits and the x-axis, so for equation 1 of table 1, it looks like figure 1. We then calculate the area of the trapezoid. Notice that the trapezoid over-estimates the true area. With enough (smaller) trapezoids we can get a very good approximation to the area under the curve (see figure 2). The sum of the area of the smaller trapezoids is the area under the curve.

The area of a trapezoid is given by: A = (h1 + h2) d

Plot graphs of the equations in table 1 for varying (input) total numbers of trapezoids. Compute and display the area between each curve and the x-axis. The number of trapezoids should be a positive integer.

Extend your app by allowing the input of varying min and max x limits beyond those in Table 1, with max >= min

Table 1: Sample curves and associated areas.

Equation	xMin	xMax	Actual Area
y = x2	1	2	2 1/3
y = x2 4	-2	2	10 2/3
y = -x3 + 6x2 x +17	2	4	80.0000
y = 2x3+2x2-5x+3	-2.5	7	65.2502

Figure 2: Area under the curve of y = x² over the range 1 to 2, with 2 trapezoids.

The more trapezoids, the better the approximation approaches the actual area. It is useful to know the error in the calculation.

The relative error can be computed by:

RE = | calculated area actual area |

actual area

%RE = | calculated area actual area | . 100%

actual area

Extend your app further by plotting %RE in area values (and the theoretical %RE line) for a range of trapezoids (1-100,000 in powers of 10 on the x-axis, 0.1-100 in powers of 10 on the y-axis) for each curve in Table 1.

Question

Week#9: App should allow input of the number of trapezoids and display correct plots of the curves for the data supplied in table 1 of the Problem Statement. Some unit tests implemented.

Answer?

I need answer from Solar2D and Lua( Special request don't do in any languages. Need in Solar2D and Lua and I need full code for this. (plz use Table 1)