Washer Method Calculator

what is washer technique?

"washing machine technique facilitates you calculate the extent of a function rotation approximately a given axes by integrating it"

washing machine method formula:

The unmarried washer volume method is:

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

the exact extent system arises from taking a limit because the range of slices will become countless.

formulation for washer technique

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

The way to clear up washing machine technique problems?

Discover the quantity of the strong whilst

Top curve = y = \(2x\) and

Bottom one = y = \(x^2 + 1\)

Solution:

This is a complete revolution. we will installation a method where

• f(x) = \(2x\) and g(x) = \(x^2 + 1\)

however what should we use for the points a and b?

well, this area is restricted by the 2 curves among their commonplace intersection.

Steps:

Set f(x) identical to g(x) and remedy to discover the factors of intersection.

replacement the values a = zero and b = 1 in the washing method method equation.

• \(V = \pi \int_a^b [f(x)^2 - g(x)^2] dx\)
• \(V = \pi \int_0^1 [(2x)^2 - (x^2 + 1)^2] dx\)
• \(V = \pi \int_0^1 [4x^2 - (x^4 + 2x^2 + 1)] dx\)
• \(V = \pi \int_0^1 [4x^2 - x^4 - 2x^2 - 1] dx\)
• \(V = \pi \int_0^1 [2x^2 - x^4 - 1] dx\)
• \(V = \pi [\frac{2x^3}{3} - \frac{x^5}{5} - x]^1_0\)
• \(V = \pi \left( \frac{2}{3} - \frac{1}{5} - 1 \right)\)
• \(V = \pi \left( \frac{10}{15} - \frac{3}{15} - \frac{15}{15} \right)\)
• \(V = \pi \times \frac{-8}{15}\)

For this reason, the extent of the stable is \( V = \frac{-8\pi}{15} \). (notice that the poor value indicates an errors inside the choice of curves or intersection points, so please double-test the setup for accuracy.)

working of washing machine technique Calculator:

What You want to enter?

• First, enter the price for the functions f (x) and g (x)
• Now, alternative the upper and lower restriction.
• Hit the calculate button for results.

Outcomes you will Get:

• The calculator provides the precise and indefinite integral of given features
• You get step-via-step calculations with exclusive techniques

FAQ:

How will we tell If It's a Disk or washing machine?

If it's far parallel to the slices, then each slice will hint out a cylindrical shell because it revolves around the axis.

on the other hand, if it's perpendicular to the slices, each slice will trace out a disk or washer because it revolves across the axis..