Set Up and Evaluate Integrals for Finding the Moment About $\rho = 1 .$

question 18

Multiple Choice

Set up and evaluate integrals for finding the moment about the y-axis for the region bounded by the graphs of the equations. (Assume $\rho = 1 .$ )
$y = 64 - x ^ { 2 } , y = 0$

• A) \( M _ { y } = 0\) by symmetry
• B)\(M _ { y } = \int _ { - 8 } ^ { 8 } \left( 64 - x ^ { 2 } \right) ^ { 2 } d x = - \frac { 262,144 } { 15 }\)
• C)\(M _ { y } = \int _ { - 8 } ^ { 8 } \left( 64 - x ^ { 2 } \right) ^ { 2 } d x = \frac { 524,288 } { 15 }\)
• D)\(M _ { y } = \int _ { - 8 } ^ { 8 } \left( 64 - x ^ { 2 } \right) ^ { 2 } x ^ { 2 } d x = \frac { 65,536 } { 15 }\)
• E)\(M _ { y } = \int _ { - 8 } ^ { 8 } \left( 64 - x ^ { 2 } \right) d x = \frac { 1024 } { 3 }\)

Differentiate between various film speeds and their visual outcomes.

Identify the principles of persistence of vision in relation to motion perception.

Understand the role of early cinema in transitioning from novelty to a popular culture phenomenon.

Recognize the impact of early cinema on subsequent film production practices.

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