Washer Method Calculator

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Introduction to the Washer Method Calculator

The washer method graph calculator is an online tool to integrate the volume of revolution. It is used for the setup of definite and indefinite integral. This disk and washer method calculator is the addition of the disk method. It is used to find the volumes of the solids of revolution.

What is Washer Method Formula Calculator

The volume of solid of revolution calculator apply the method of exact disc method and the disk method formula to find the cross-dimensional area and the volume of revolution of different shapes.

washer method calculator with steps

The washer integral calculator works online to find the solid of revolution. It takes the raw data from the user in the form of input and then gives you the calculated result accurately and timely.

For those who are looking for a more advanced method of calculating the volume of revolution, the cylindrical shells calculator may be of interest. Similar to the Washer Method, the Shell Method provides an effective way to find the volume, but it uses a different approach.

Formula Used by Washer Volume Calculator

A washer method calculator is like a disk but with a center, the center hole cut out. The volume revolution formula of a washer method requires an outer radius of r1 and an inner radius of r2.

The single washer volume formula is:

$$ V = π (r_2^2 – r_1^2) h = π (f (x)^2 – g (x)^2) dx $$

The exact volume formula appears by taking a limit as the number of slices becomes uncountable.

Formula for washer method graph calculator is as follow:

$$ V \;=\; π \int_a^b [f(x)^2 – g(x)^2] dx $$

Another method for calculating the volume of revolution is the Disc Method. This method involves slicing the 3D object into thin discs and adding up their volumes to find the total. If you're interested in exploring this method, our volume disk method calculator provides a simple and intuitive way to use this approach.

How Washer Calculator Solve for Volume of Solid of Revolution?

This washer volume calculator uses the above formula to provide all possible steps for required query of user.

Let's see an example how it may work.

Example of Washer Method

Example: Find the volume of the solid, when the bounding curves for creating the region are outlined in red. The top curve is f(x) = x and the bottom one is y = x3

This is a complete revolution. We will set up a formula where f(x) = x and g(x) = x2. But what should we use for points a and b?

Well, with some area problems, you may need to find limitations. This area is limited by the two curves between its common intersection. Set f(x) to g(x) and find to locate the points of intersections.

Note: Area between two curves may also calculate using our area integral calculator.

Substitute the a = 0 and b = 1 in the washer method equation.

$$ V \;=\; π \int_a^b [f (x)^2 – g (x)^2] dx $$ $$ V \;=\; π \int_0^2 [ (x)^2 – (x^3) ^2] dx $$ $$ V \;=\; π \int_0^2 [ x^3 – x^6] dx $$ $$ V \;=\; π [ \frac{(x)^4}{4} – \frac{(x)^7}{7} ]^2_0 $$ $$ V \;=\; \frac{328π}{21} $$

And here you get the volume of solid of revolution with all possible steps that we offer in every tool of this integration solver.

How does Washer Method Solver Work?

The online washer method calculation determines the definite integral of the volume of revolution. So, it will be named as volume by washer calculator.

Insert:

  • First of all, Enter the value for the functions f (x) and g (x).
  • Then, add the upper limit and lower limit.
  • Click the calculate button for results. The results are shown on your screen.

Outcome:

The disk/washer method calculator provides the step by step integral volume of the given functions.

Related: The Simpson Rule is a numerical integration method that is used to approximate the definite integral of a given function. If you're looking for an efficient way to find the area under a curve, the Simpson Rule Calculator can help.

Benefits of Washers Method Calculator with Steps

The disk and washer method calculator is an online tool that is mainly used to evaluate the area of a solid of revolution. The volume of the solid of the revolution calculator is used to find out the volume of every chunk of the solid shape. It calculates the volume of the solids concerning the axis parallel to the revolution axis.

  1. The volume of revolution is best evaluated by using this integration tool.
  2. It finds the best volume of the revolution for irregular shapes.
  3. The disk and washer method calculator are easy to use and understandable.

While the Washer Method and the improper integrals calculator may seem unrelated at first glance but both are used to calculate the volume of a 3D object.

How to Find this Washer Integral Calculator?

To find the washer method or volume revolution calculator you have to:

  1. Open your browser’s home screen.
  2. Enter the calculator keywords like "volume by washer calculator","volume washer method calculator" in the search bar and search for the results.
  3. Now select the required calculator from the Google suggestions.
  4. Then enter the values in the required fields.

This volume of solid of revolution calculator is easy to use for students and other people. If we try to solve them manually it takes much time. But online calculators make it easier and quicker. It helps users to find out about the volume revolution without any real-time issues.

Frequently Asked Question

How do you know when to use the washer method?

If you want to find the volume of any shape obtained when rotating the region bound by f(x), y=1, and x=2 about the y-axis, then you would utilize the washer method till then the shape you want to get after rotating has a center hole in it.

Why is it called the washer method?

Well, it's going to be equal to dx. And let's rotate that whole thing around the x-axis. So, if you rotate the shape around the x-axis, then it ends up with a disk/ washer method. So, this method is named the Washer Method.