Question

6. Find the exact coordinates of the centroid of the region bounded by y = x? and x = y3. (12 points)

Answer 1

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) and (1,1) Tusersection limit of to how Area А. S (x3 - x2) dx 0 WA 3 3 x x 4. MIT - الي 5 12 b . Mow My 11 Sx (fin) – g(x)) du al xes 20

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 x5 online 2 5 3 Mx 5

We 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 Function If It satisfy s f(x) dx - Now ser) de & tc²x²

T tant cex) ->)] 1 I ( tem (0) tant (-o) => (-)) = ņ ñ fex) is probability density function of car