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6. Find the exact coordinates of the centroid of the region bounded by y = x?...


6. Find the exact coordinates of the centroid of the region bounded by y = x? and x = y3. (12 points)
1 8. Let f(x) = For what value of c> 0 is fa probability 1+c2x2 density function? (8 points)
6. Find the exact coordinates of the centroid of the region bounded by y = x? and x = y3. (12 points)
1 8. Let f(x) = For what value of c> 0 is fa probability 1+c2x2 density function? (8 points)
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6. y = x² and x=43 = x3 y = x2 Now Interesection point 2-43 x=y3 1,1) yan 22 (0,0) x 3 re2 = x5 *(1-x5)=0 4 3209 points coo)My 13 Sex -~39. My 7 3 x 3 7 T 7. 4 1 28 We know 5 My 12 28 11 3 7 A 28 bles 1 MIN Now Mra j(x)2-1022 2 0 2 ( x 4 ) dx 5 3 x5We know 11 Max A 11 5 12 ý 12 25 centroid : (x, y) 12 3 7 25 ful It c2 x2 we know A function is probability density FunctionT tant cex) ->)] 1 I ( tem (0) tant (-o) => (-)) = ņ ñ fex) is probability density function of car

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6. Find the exact coordinates of the centroid of the region bounded by y = x?...
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