Use the Shell Method to Set Up and Evaluate the Integral

question 6

Multiple Choice

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. $y = x , y = 0 , x = 20$

• A) \(V = 2 \pi \int _ { 0 } ^ { 10 } ( y ) ( 20 - y ) d y = \frac { 40,000 } { 3 } \pi\)
• B) \(V = 2 \pi \int _ { 0 } ^ { 10 } ( y ) ( 10 + y ) d y = \frac { 40,000 } { 3 } \pi\)
• C) \(V = 2 \pi \int _ { 0 } ^ { 20 } ( y ) ( 10 + y ) d y = \frac { 8,000 } { 3 } \pi\)
• D) \(V = 2 \pi \int _ { 0 } ^ { 20 } ( y ) ( 20 - y ) d y = \frac { 8,000 } { 3 } \pi\)
• E) \(V = 2 \pi \int _ { 0 } ^ { 10 } ( y ) ( 20 + y ) d y = \frac { 4,000 } { 3 } \pi\)

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Definitions:

Means

Refers to the arithmetic averages of data sets, representing the central or typical value in those sets.

Interaction Effect

The effect on a dependent variable that arises from the combination of two or more variables, different from the sum of their separate effects.

Main Effect

The direct influence of an independent variable on a dependent variable in an experiment.

Simple Effect

A statistical term that describes the effect of one factor at a specific level of another factor within an ANOVA test.