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# 美国代写|微积分代写Calculus Assignment代写|Tables of Integrals and Use of Technology

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## 美国代写|微积分代写Calculus Assignment代写|Using fechnology

For decades, from room-size computers to early microcomputers to laptops to smartphones and beyond, computer algebra systems (CASs) have been available to assist in mathematical computations. We don’t even have to know a software package’s picky syntax anymore, because these software packages have become more user friendly, and search engine capabilities have made the task so easy, that many antiderivatives can be found merely by asking your favorite assistant verbally. However, there are still advantages to using a CAS in typed form, and the relative ease of written precision compared to using verbal language may make those advantages persist.

Another fact that may persist is that the algorithms implemented in software to compute antiderivatives are not always the same algorithms taught in calculus classes. For this reason, those of you using a CAS to check an answer may be confused by the result. One strategy for handling the discrepancy is based on the fact that any two antiderivatives of a function must differ by a constant. Take the answer given by the CAS, subtract your antiderivative, and determine whether the answer is a constant.

Example 1 A student has computed the value of $\int \sin ^{3} x \cos ^{5} x d x$ as
$$\frac{\sin ^{4} x}{4}-\frac{\sin ^{6} x}{3}+\frac{\sin ^{8} x}{8}+C$$

## 美国代写|微积分代写Calculus Assignment代写|Tables of integrals

What did people do before technology was readily available? Just as you may have compiled a list of antiderivative formulas to help you organize your material, during the development of calculus, much larger lists of antiderivative formulas were compiled to make finding antiderivatives more efficient. Entire books were published containing nothing but antiderivative formulas! Such a list is called a table of integrals. Tables of integrals have appeared in calculus texts for centuries, and although their need has passed, the tradition has not. Table 1 , a table of integrals (which looks more like a list) appears on the next few pages, organized by type of function.

Using a formula from a table of integrals is no different than using any other antiderivative formula. Formulas in the table are written using the variable $u$; all other letters are assumed to be constants. The constants may be either positive or negative, unless specifically indicated otherwise. The majority of the formulas in the table of integrals are copied from GSL.

Example 3 Use a formula from the table of integrals (see Table 1) to evaluate $\int \sqrt{9+x^{2}} d x$.

Solution Because the integrand contains $9+x^{2}$ we look in the section of the table with the heading “Forms Containing $a^{2}+u^{2}$.” There we find formula #89:
$$\int \sqrt{a^{2}+u^{2}} d u=\frac{u}{2} \sqrt{a^{2}+u^{2}}+\frac{a^{2}}{2} \ln \left(u+\sqrt{a^{2}+u^{2}}\right)+C .$$

## 美国代写|微积分代写CALCULUS ASSIGNMENT代写|TABLES OF INTEGRALS

∫一个2+在2d在=在2一个2+在2+一个22ln⁡(在+一个2+在2)+C.

## 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。