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Washer Method Calculator

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by Alan Walker

Last Updated August 16, 2022

Introduction to Washer Method Calculator

Washer method calculator is an online tool for calculating the volume of a solid of revolution of a solid-state material. It is also known as volume of solid of revolution calculator. It helps a user to integrate along axis "parallel" to the axis of revolution. So that you can easily find volume using washer method calculator

Integration is very important for students to learn as it is used extensively in routine life. Just like other online calculators, integration solver tools are also very important as they help to get the accurate answer of any equation.

How to find Washer Method Formula Calculator?

In this age of technology it is super easy to find anything you want. If you are looking to find washer integral calculator, you have two options through which you can find it easily. Either you can search online to find our volume by washer method calculator. Or you can search for integral-calculator.com and find our washer calculator from there.

Apart from offering this calculator, you can find other integration related calculators like fourier transform calculator with steps and laplace calculator with steps. This website offer a lot of other integration tools for you to learn and practice online. These tools are quick, accurate and free to use.

How Does the Washers Method Calculator Work?

Washer calculator is an online way of calculating so it needs to have internet connection to perform. The volume washer method calculator takes the input from the user and compute these on our servers. After that it shows you accurate result of your equation or query.

Related: Also find other useful calculators on this website like shell method solver and method of disks calculator and get instant and accurate results.

Area of a Washer Calculator Input

The input values include

  1. Value of f(x)
  2. Value of g(x)
  3. Upper Limit
  4. Lower Limit

Related: Read this useful blog to learn integration by partial fraction in 5 minuets.

Washer Method Calculator Output

After taking all the inputs, the washer volume calculator shows you the output which include

  1. The solid of revolution calculator provides a step-by-step methodology for determining the volume using washer method integration.
  2. The volume of revolution calculator shows you results of indefinite integration and definite integration.

This website also offer indefinite integral calculator and definite integral calculator which you can use to increase your efficiency regarding evaluating integrals.

How to use Washer Method Formula Calculator?

Washer method calculator with steps finds the volume of solid of revolutions. The solid of revolution calculator is very easy to use. You just need to follow the below procedure:

  1. Enter the value of f(x) in first input
  2. Enter the value of g(x) in second input
  3. Entner the value of Upper Limit
  4. Enter the value of Lower Limit
  5. Click on Calculate button

Once you click on the calculate button, washer method calculator will instantly calculate the volume of solid revolutions and show accurate results step by step.

Frequently Asked Questions

What is the Washer Method Formula?

The washer method in calculus, is known as disk integration of objects of revolution. It is a method of integrating a solid to find its volume of revolution. It calculates the volume of revolution by integrating along an axis parallel to the axis of rotation. The washer method formula is used to find volume of revolution, that is,

$$ V \;=\; \int_a^b 𝜋 (R^2 - r^2) dx

Where,

  • r= is the radius of inner slice.
  • R= is the radius of outer slice.

You can also use volume of revolution calculator above to instantly find accurate results with steps and graph.

Is Disk and Washer Method the Same?

The disk method is used to find the volume of revolution of a solid by finding the area of its disk shape slices. It is used to find volume of revolution for those solids that do not have hole as like a disk.

The washer method is the modification of disk method that covered the solid of revolution with holes. You can use area of a washer calculator for finding volume of revolution of solid.

What is the Difference Between Shell and Washer Method?

The shell method is a method of finding volume of a solid of revolution. It calculates the volume by integrating along the axis perpendicular to the axis or rotation. The formula of shell method is,

$$ V \;=\; 2𝜋 \int_a^b r(x)h(x) dx $$

Where,

  • r(x)represents distance from the axis of rotation to x.
  • h(x)represents the height of the shell.

Whereas the washer method is the modification of disk method that find the volume of revolution by integration along the axis parallel to axis or revolution.

It is best for those solids of shape like shell having hole inside. The washer method formula is,

$$ V \;=\; \int_a^b π(R^2−r^2)dx $$

Where,

  • r = is the radius of inner slice.
  • R= is the radius of outer slice.

What is the Purpose of Washer Method?

The main purpose of washer method is to find the area of a solid of revolution with a shell shape. The method integration is used to find volume of every slice of the solid along an axis parallel to the axis of revolution.

It is best for finding volume of revolution for object having gap inside. You can find it manually or use washer method graph calculator with steps.

How to Find Radius in Washer Method?

In washer method, two radii are used to find volume of revolution. One radius is of inner slice and other is for outer slice. Suppose the following problem to understand how to find R and r in washer method.

Example:

By integrating with respect to the variable y, find the volume of the solid of revolution formed by rotating the region bounded by y = 0, x = 4 and y = √ x about the line x = 6.

First we sketch the graph of the given problem as,

The solid region is rotation about y-axis at x=6. So we will have a washer shape and inner radius of shell is r and outer radius is R. In this example, we will find the inner radius by the distance between the line x = 4 and the line x = 6, so r = 2.

The outer radius R is the horizontal distance between the graph of y=√x and the line x = 6. So, we have.

R = 6 - y2

Because,

y2 = x

Now by using washer method,

$$ V \;=\; \int_a^b π(R^2−r^2)dy $$ $$ V \;=\; \int_a^b π((6-y)^2−2^2)dy $$ $$ V \;=\; \int_a^b π((36-12y^2+y^4)−4)dy $$

By integrating, we get,

$$ V \;=\; π \Biggr|(36y-4y^3+ \frac{y^5}{5})−4y) \Biggr|_0^2 $$

We get,

$$ V \;=\; \frac{192}{5}π $$

We hope this article helped you to understand washer method and its calculation. Also find double integrals calculator and triple integrals calculator on this website to learn more about multivariable integrals.

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