Posted on Categories:Calculus Assignment, 微积分, 数学代写

# 数学代写|微积分代写Calculus代考|Approximating area with right sums

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 数学代写|微积分代写Calculus代考|Approximating area with right sums

Now let’s estimate the same area under $f(x)=x^2+1$ from 0 to 3 with right rectangles. This method works just like the left sum method except that each rectangle is drawn so that its right upper corner touches the curve. See Figure 8-6.

The heights of the three rectangles in Figure $8-6$ are given by the function values at their right edges: $f(1)=2, f(2)=5$, and $f(3)=10$. Each rectangle has a width of 1 , so the areas are 2,5 , and 10 , which total 17. Table 8-2 shows the improving estimates you get with more and more right rectangles.

Estimates of the Area under $\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^2+\boldsymbol{1}$ Given by Increasing Numbers of “Right” Rectangles
\begin{tabular}{ll}
Number of Rectangles & Area Estimate \
\hline 3 & 17 \
6 & 14.375 \
12 & $\sim 13.156$ \
24 & $\sim 12.570$ \
48 & $\sim 12.283$ \
96 & $\sim 12.141$ \
192 & $\sim 12.070$ \
384 & $\sim 12.035$ \
\hline
\end{tabular}

## 数学代写|微积分代写Calculus代考|The Right Rectangle Rule

The Right Rectangle Rule: You can approximate the exact area under a curve between $a$ and $b, \int^b f(x) d x$, with a sum of right rectangles given by the following formula. In general, the more rectangles, the better the estimate.
$$R_n=\frac{b-a}{n}\left[f\left(x_1\right)+f\left(x_2\right)+f\left(x_3\right)+\ldots \ldots \ldots . .+f\left(x_n\right)\right]$$
where $n$ is the number of rectangles, $\frac{b-a}{n}$ is the width of each, and the function values are the heights of the rectangles.

If you compare this formula to the one for a left rectangle sum, you get the complete picture about those subscripts. The two formulas are the same except for one thing. Look at the sums of the function values in both formulas. The right sum formula has one value, $f\left(x_n\right)$, that the left sum formula doesn’t have, and the left sum formula has one value, $f\left(x_0\right)$, that the right sum formula doesn’t have. All the function values between those two appear in both formulas. You can get a handle on this by comparing the three left rectangles from Figure 8-4 to the three right rectangles from Figure 8-6. Their areas and totals, which we calculated earlier, are
Three left rectangles: $\quad 1+2+5=8$
Three right rectangles: $2+5+10=17$

The sums of the areas are the same except for the left-most left rectangle and the right-most right rectangle. Both sums include the rectangles with areas 2 and 5 . Look at how the rectangles are constructed – the second and third rectangles in Figure 8-4 are the same as the first and second rectangles in Figure 8-6.

## 数学代写|微积分代写Calculus代考|Approximating area with right sums

\begin{tabular}{ll}
Number of Rectangles & Area Estimate \hline 3 & 17 \6 & 14.375\12 &$\sim 13.156$ \24 &$\sim 12.570$ \48 &$\sim 12.283$ \96 &$\sim 12.141$ \192 &$\sim 12.070$ \384 &$\sim 12.035$ \hline
\end{tabular}

## 数学代写|微积分代写Calculus代考|The Right Rectangle Rule

$$R_n=\frac{b-a}{n}\left[f\left(x_1\right)+f\left(x_2\right)+f\left(x_3\right)+\ldots \ldots \ldots . .+f\left(x_n\right)\right]$$

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。