Shell method(壳方法)和Washer method(洗衣机方法)是微积分中用于计算旋转体体积的两种方法。 Shell method(壳方法)是一种通过将旋转体切割成无限多个薄壳(或者说管壳)来计算体积的方法。具体而言,我们将旋转体沿着垂直于旋转轴的方向切割成无数个薄壳,每个薄壳的厚度非常小。然后,我们计算每个薄壳的体积,并将所有薄...
shell method和washer method -回复 什么是壳法和洗衣机法? 壳法和洗衣机法是微积分中求解旋转体体积的两种方法。这两种方法都可以用来计算由曲线绕坐标轴旋转一周所形成的旋转体的体积。壳法和洗衣机法是数学家们为了解决这类问题而发展出的两种重要的求解途径。 壳法(shell method)也被称为圆盘法。它的基本...
Are the disk and washer methods the only way to find the volume of a solid of revolution? Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher) Absolutely not! What Is The Shell Method The shell method, sometimes referred to as the method of cylindrical shells...
Question: Use both the washer method and the shell method to find the volume of the solid that is generated when the region in the first quadrant bounded by y=x2,y=25, and x=0 is revolved about the line x=5.within your choice....
This means that through the shell method, we have V=4π. Meaning, the volume of the solid formed by revolving the area under the curve of y=1x from x=1 to x=3 is equal to 4π. When to use the shell method? Although the disk and washer methods are more straightforward than the ...
答:当旋转体是由曲线绕某条轴旋转而成时,我们可以使用Shell method。当旋转体是由两条曲线之间的区域旋转而成时,我们可以使用washer method。 问题2:如何确定薄壳或洗盘的高度和厚度? 答:薄壳或洗盘的高度可以看作是x轴上的横坐标x到旋转曲线的距离。它可以通过f(x)或f(x)-g(x)来计算。薄壳或洗盘的厚度可...
Shell Method和Washer Method是微积分中计算旋转体体积的两种重要方法。Shell Method适用于计算由曲线围绕某轴旋转形成的“壳状”立体图形的体积,而Washer Method则适用于计算由两条曲线围绕某轴旋转形成的“环状”立体图形的体积,特别是当内部存在空心时。理解和掌握这两种方法,可以帮助我们更有效地解决各种复杂的几何体...
Here is another method for finding the volume of a solid of revolution.It's called the method of cylindrical shells or the shell method.For many problems,it's easier to apply than the disk method and washer method.So,what is a shell?A shell is a solid bounded by two concentric right ...
The volume of a revolution can be calculated using the slicing method, the disk method, and the washer method. Explore the processes of the three methods and discover how to use them to find the volumes of revolution. Related to this QuestionUse...
10. Use the disk/washer OR the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given line. Include a sketch of the graph of the regions. List which method ...