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 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.
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
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= | distance between the function and the axis of rotation |
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= | upper limit |
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= | lower limit |
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= | 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”
Volume of a torus
Revolution of an area between two 2D curves to form a solid
Revolution about an off-axis line
Washer method: revolving around x- or y-axis
washer method calculator y axis
washer method calculator x axis
washer method calculator with steps
washer method calculator emath
FAQ
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