Washer Method Calculator


What is Washer Method?

This process is a logical extension of the disk method for determining the volumes of the solids of revolution. Use the Washer Method to set up the definite and indefinite integral that provides the volume of the revolution. The washer method is used to discover the volume enclosed between two functions. In this method, we cut the region of revolution perpendicular to the axis of revolution. We call it as Washer Method because the slices got in this way form washers. Washer Method Calculator is tool used to discover the volume enclosed between two functions

Washer Method Calculator

Washer Method Formula

A washer is the same as a disk but with a center, the hole cut out. The formula of volume of a washer requires both an outer radius r^1 and an inner radius r^2.Washer Method Formula

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 arises from taking a limit as the number of slices becomes infinite.

Formula for washer method V = π ∫_a^b [f (x)^2 – g (x)^2] dx

Formula
\pi \int _{a}^{b} R (x)^2 \; dx
R(x) = distance between the function and the axis of rotation
a = upper limit
b = lower limit
dx = slides along x

 

How Washer Method Calculator Works?

An online washer calculation finds the definite and indefinite integral of the volume of revolution

Input:

  • First, Enter the value for the functions f (x) and g (x)
  • Now, substitute the upper and lower limit.
  • Hit the calculate button for results.

Output:

  • The “washer” method calculator provides the definite and indefinite integral of given functions.
  • The calculator does step-by-step calculations with different methods.

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

$$ V = π ∫_a^b [f (x)^2 – g (x)^2] dx $$

$$ V = π ∫_0^1 [ (x)^2 – (x^2)^2] dx $$

$$ V = π ∫_0^1 [ (x)^2 – (x)^4] dx $$

$$ V = π ∫_0^1 [(x)^2 – (x)^4] dx $$

$$ V = π [(x)^3 / 3 – (x)^5 / 5]^1_0 $$

$$ V = 2 π / 15 $$

 

Area of a “washer”

washer method calculator with steps

Volume of a torus

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washer method calculator y axis

 

washer method calculator

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Revolution about an off-axis line

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Washer method: revolving around x- or y-axis

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washer method calculator x axis

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FAQ

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