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Use the Shell Method to Find the Volume of the Solid

question 33

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Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis.
- y=5x3,y=5x, for x0y = 5 x ^ { 3 } , y = 5 x \text {, for } x \geq 0


Definitions:

Scatter Diagram

A graphical representation that shows the relationship between two quantitative variables by plotting data points on a two-dimensional plane.

Least Squares Regression

A statistical method used to find the best-fitting line through a set of data points by minimizing the sum of the squares of the vertical distances of the points from the line.

Coefficient of Correlation

A mathematical gauge that assesses the strength of the bond between the relative movements of two variables.

Sum of Squares

A statistical measure that quantifies the variability or dispersion of a set of numbers by squaring their deviations from the mean.

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