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Find the Centroid Of D={(x,y)∣x2a2+y2b2≤1,y≥0}D = \left\{ ( x , y ) \mid \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } \leq 1 , y \geq 0 \right\}

Question 77

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Find the centroid of D={(x,y)∣x2a2+y2b2≤1,y≥0}D = \left\{ ( x , y ) \mid \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } \leq 1 , y \geq 0 \right\} , the region enclosed by the upper half of the ellipse x2a2+y2b2=1\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 .

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