shell method和washer method 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
现在,我们来回答一些与Shell method和washer method相关的问题。 问题1:什么时候使用Shell method,什么时候使用washer method? 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:...
Meanwhile, for the shell method, we can see that all we need is to evaluate the integrate $x(x^2 + 4)$ with respect to $dx$ from $x=0$ to $x=4$. Washer Method \begin{aligned}V&= \pi\int_{0}^{4} (4^2 -0^2)\phantom{x}dy + \pi\int_{4}^{20} [4^2-(\sqrt{y...
y=2x2−x3 and y=0 First, let’s graph the region and find all points of intersection. Shell Method Formula (Around Y-Axis) And we quickly notice that if we tried to use the washer method, our “top” (outer) function is the same as the “bottom” (inner) function, which means...
Learn what the shell formula is. Understand when to use the shell method and how to derive the shell method formula. Practice using the shell...
Shell method和washer method是数学中用于计算旋转体体积的两种方法,常用于微积分课程中。它们在实际问题的建模和求解中都有广泛的应用。 首先,让我们详细了解shell method。Shellmethod(壳法)是一种通过将旋转体切割成无数无限薄的壳体来计算体积的方法。这些壳体垂直于旋转轴,其厚度非常薄,可以将其近似为线段。通过将...
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...
Answer to: Use the shell method to find the volume of the solid generated by revolving the region bounded by the curves y = 3x, y = 0, and x = 2...
The invention discloses a loudspeaker device and method for manufacturing a shell of the loudspeaker device. According to the loudspeaker, a side washer and a conductive element are integrally combined with the shell in an injection molding mode, so that combination firmness of the side washer, ...
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 Question ...