What is the Difference Between Washer and Shell Method Integration?

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washer and shell method integration

Introduction

Calculus is the branch of mathematics that deals with both differential and integral calculus. The integral calculus can define as the study of applications of integrals, properties and determination.The washer method and shell method are also studies of integrals calculus. The method of slicing refers to the washer method whereas the findings of the volume of the solid of revolution refers to the shell method. The revolution of solid and different objects that are necessary in the washer method and shell method are to discussed in this study. This article will give you the proper orientation of the washer method and shell method, their major differences and understandings. The student will be able to learn about the basics of the washer method and shell method briefly via this article.

What is the Washer method?

It is well understood that the definition of the washer method is the application of the method of slicing. It is also known as the process that helps in finding the volume of objects of revolution. In simple words it can said that it is the method which used to find the volume of solids of revolution. The washer method acts as the function that takes on the interval ( x and y ) and then rotates at some point. Specifically to find the volume of the solid that has two disks which leads to the two disc method used to find the volume.

What is the Shell method?

The method which used to find the volume of a solid of the revolution has called the shell method. Because the shell method uses the cylindrical shells. It is best saying that the shell method in calculus refers to the method of finding the volumes of a shape. In simple words the shell method has used when the integration along the axis is perpendicular to the axis of revolution, to calculate the volume of a solid of revolution. All the objects that occupy space and physical dimensions of the objects measured by these shell methods. You can also calculate shell methods online from the cylindrical shell volume calculator.

Differences between the washer method and shell method

  • The washer method is finding the volume of objects of revolution and the shell method is finding the volume of a solid of the revolution.
  • The washer method used when the solid has holes in the middle and the shell method used when the solid has holes in it. For example, the washer method used when the solid object is like the CD that has a hole in the centre or in the middle and the shell method used when the solid resembles a toilet paper tube that has hole in it.
  • The representative rectangle of the washer methods are perpendicular to the axis of the revolution and the representative rectangle of the shell methods are parallel to the axis of the revolution.
  • The washer method has used in evaluating the revolutions around the x-axis and the shell method has used in evaluating the revolutions around the y-axis.
  • The washer method explained by the revolution along the x-axis at each x varying the radii and shape whereas the shell method explained by 2πx where the x belongs to radius of circle and varying thickness and shape f ( x ).
  • The washer method used to find the volumes between the two functions and the shell method used to calculate the volume of revolution by summing up the volumes of cylinder shells in limits.
  • The orientation of the washer method is perpendicular to the axis and the shell method is parallel to the axis.
  • The washer integration method uses the disk method twice as it uses to find the exterior volume and to subtract the interior volume whereas the shell method uses the area beneath the curve and rotates it to create a cylinder instead of a circle.
  • The solid of revolution by washer refers to the conceives of volume as the summation of circular cross-sections for some given lengths and the shell method refers to the conceives of volume as the tightly packing shells together of various sizes.

If you are still confused about how to solve them, use a shell method calculator and a washer integral calculator.