SolutionGiven y=7x2+6x,y=0,x=0,x=6
dA=7x2+6xxˉ=∫06dA∫06xdA=xˉ=∫06(7x2+6x)dx∫06x(7x2+6x)dx=∫067x2dx+∫066xdx∫067x3dx+∫066xdx=[37x3]06+[26x2]06[47x4]06+[26x2]06=[37(64−0)]+[26(64−0)][47(64−0)]+[26(64−0)]xˉ=504+1082268+108=6122376=3.88
yˉ=∫06dA∫06ydA=yˉ=∫06(7x2+6x)dx∫06(7x2+6x)2dx=∫067x2dx+∫066xdx∫0649x4dx+84x3+36x2=[37x3]06+[26x2]0649(5x5)06+84(4x4)06+36(3x3)06=[37(6)3]+[26(6)2]49(565)+84(464)+36(363)yˉ=504+10876204.8+27216+2592=612106012.8=1732.23∴(xˉ,yˉ)=(3.88,1732.23)
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