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)\(M _ { y } = \int _ { - 8 } ^ { 8 } \left( 64 - x ^ { 2 } \right) d x = \frac { 1024 } { 3 }\)

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