Disc Method Calculator


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Introduction to the Disk Method Calculator

A disk method volume calculator is an online tool that is used to calculate the volume of any object which is three-dimensional in structure by comprising it into smaller parts or disks. This online tool that takes the input from the user and then gives a detailed solution with the step-by-step elaboration of the results.

The volume of disk calculator calculus is an excellent tool to determine the volume of any cylindrical shape having upper and lower functions and the limits of that integral.

If you're looking to calculate the volume of a solid using integration, our volume by disk method calculator and volume by washer calculator are two great tools to help you out!

What is the Disc Method Calculator?

The volume of a disc calculator is the tool to calculate the volume of solid of revolution when integrating along an axis parallel to the axis of revolution. The disk volume calculator is a wonderful tool that gives accurate and precise results in a few seconds.

disc method calculator with steps

This calculator gives you a step by step answer having two sections in it

  • First is in the form of answer that simple evaluate Definite Integral,
  • Next part is the answer with possible intermediate steps.

The volume disk method calculator is also called a disc method calculator, solid of revolution calculator, or volume of the calculator.

Whether you prefer the disc, washer, or shell method, our suite of integration calculators has got you covered! Use our cylindrical shell volume calculator to easily compute the volume of a solid of revolution.

Formula used by Disk Method Volume Calculator

Let R1 be the region bounded by y = f(x), x = a, x = b and y = 0. Suppose we form a solid by revolving it around the x-axis. The volume of the solid is given by:

$$ V = π \int_a^b [f(x)]^2 dx $$

How to Find Volume by Disk Method

The disk method of integration uses the above written formula to find the volume of solid of revolution by spitting in it circular disk forms:

Let's see it with an example:

Example: Let R be a region bounded by y=x2, x=−2, x=3, and x-axis. Find the volume of the solid obtained by rotating the region R about the x-axis.


The volume is given by

$$ V \;=\; \int_{-2}^3 [π(x^2)]^2 dx $$ $$ V \;=\; π \int_{-2}^3 (x^4) dx $$ $$ V \;=\; π \left[ \frac{x^5}{5} \right]_{-2}{3} $$ $$ V \;=\; 55π $$

How does Volume by Slicing Calculator Work?

The disc method calculator takes inputs from the user in terms of upper function, lower function, upper bound and lower bound limits in the required fields. It is fairly easy to use its easy-to-use interface. The user enters all the essentials in the required fields and after that, just click the submit option to get the solution. This disk method calculator gives the user accurate and precise solutions to their integrable problems.

Here are step-by-step instructions for how this disc volume calculator works:

Step 1: First, look over your objectives and trace out the axis upon which the revolution of the solid object takes place. In the revolution of the volume calculator, the revolution axis will then set the basis for the limits of the integral function.

Step 2: Now enter all the necessary data values into the assigned input boxes. Enter the lower and upper limit in the input space titled "From" and "To," respectively.

Step 3: Then, enter the raw values in the given two input data boxes. Now enter the object's upper and lower functions in the disc integration calculator in the assigned input boxes.

Step 4: Once you have kept all the input values, click on the "calculate."

The Disk Method Calculator will take only a few seconds and give you the required solution.

Related: Need to approximate the definite integral of a function? Our trapezium rule calculator is a simple and effective tool for estimating area under a curve with straight line segments.

The answer is categorized in two forms, which are as below:

Indefinite Integral Form

The first portionof calculation of Disk Method Calculator or Volume by splicing calculator provides the exact. This form shows the solution without considering the limits and hence gives the final solution in order with the variable x and a constant c.

Definite Integral Form

The second form in which the volume of disk calculator calculus or Volume by splicing calculator gives you the answer is in the form of a definite integral. This solution provides the calculation of exact volume for the given function as like convergent or divergent integral calculator.

Benefits of Disc Integration Calculator

The disc method calculator is an available online tool that is free. It makes the life of the students and users easier. It is available worldwide and is free of cost. It generates authentic and precise results. The volume by slicing calculator releases the stress of the long hectic integration problems.

  • Accuracy
  • Time-Saving
  • Fast
  • Stress Relieving
  • Easy to Use
  • Free of cost
  • Understandable

A disc volume calculator is a wonderful tool for splicing objects to calculate their volumes.

Computing the area under a curve has never been easier with our graph area calculator. Simply input your function and bounds, and our tool will quickly provide you with the accurate result you need!

Is it Reliable to Use Volume of a Disc Calculator?

The disc method calculator is a great tool to find the volume of solid of revolution with the step by step solution. This online tool provides 100% accurate answer without charging any cost.

When we talk about the reliability, the disc integration calculator is the great reliable and accurate tool. Disk volume calculator provides possible intermediate steps along with graphs. This tool is verified by expert mathematicians of Integration calculator.

So, be connect with our integrals solver to stay tunned for a new calculus relevant tools. Must try our all new long division calculator with steps for solving division under the integration.

Frequently Asked Question

What is the difference between the disk method and the washer method?

The disk method and the washer method are two techniques used to find the volume of a solid of revolution. The main difference between them is the shape of the cross-sectional area used to compute the volume. The disk method uses circular disks, while the washer method uses washers or annuli, and is typically used when there is a hole or a region removed from the solid.

Do the shell and disk methods give the same answer?

Yes, the disk and shell methods yield the same result when used to compute the volume of a solid of revolution. Both methods are based on the same principle of adding up infinitesimally small volumes to find the total volume of the solid, and the only difference is the shape of the small volume elements used in the integration.

How do you calculate disk volume?

To calculate the volume of a solid using the disk method, you need to follow these steps:

  1. Determine the axis of rotation: This is the line around which the region is being rotated to form the solid.
  2. Identify the region: Determine the boundaries of the region in terms of the variable being integrated.
  3. Integrate: Use the formula V = ∫(πr^2)dx, where r is the distance from the axis of rotation to the curve and x is the variable being integrated.