Provide an Appropriate Response $y$ -Axis to Generate a Solid $y = x$

question 197

Essay

Provide an appropriate response.
-The region shown here is to be revolved about the $y$ -axis to generate a solid. Which of the methods (disk, washer, shell) could you use to find the volume of the solid? How many integrals would be required in each case?


$y = x$
$y = 4 x - x ^ { 2 }$

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Definitions:

Covariance

A measure that indicates the degree to which two variables change together. If the variables tend to show similar behavior, the covariance is positive; if they show opposite behavior, the covariance is negative.

Standard Deviation

A system for measuring the degree of difference or spread in a set of figures.

Scatterplot

A graphical representation of two variables on a set of Cartesian coordinates to investigate the relationship between them.

Independent Variable

An experimental or study factor that is altered to determine its impact on a variable that depends on it.