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,每个薄壳的厚度非常小。然后,我们...
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...
the solid obtained by revolving the region bounded by the curves of $y = x^2 + 4$, $y =0$, $x=0$, $x =4$, and about the $y$-axis. To appreciate the simplicity of the shell method, let us show youhow we revolve the region using the washer method versus the shell method....
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 they would eliminate each other! Therefore, rather than using rectangles perpendicular to the axis...
Use the shell method for (a) and washer method for (b). Volume of Solid of Revolution: Note that in cylindrical shell method the formula is V=2π∫abrhdr where r is the centroid of the region...
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 -回复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 ...
Find the volume of the solid generated by revolving the region bounded by x = 5/7, x = -5y, and y = 1 about the line y = 1. Use the shell or washer method.Disk Method in Calculus:In order to determine the ...
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 y...
Answer to: Consider the region bounded by y=x-x^2 and y=0 rotated along the y-axis. Solve using either the disk, washer, or shell method. By...