## Answers

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•Cos(x) +2.

R=0.5 in. 2.2 in ke 2 in 2 in od T. YdA E AY sy JdA EA А, 9, Ý = Ay, A2₂ A,+A₂ A3 (oux2.2) ( 22 ) A4, = = 9.68 inch? Adx A2 = 1922 ly A= yda Ay = y.dxxy AzY₂ = da -2 y = f(x) = Cos(x) + 2 [ Cocos (2) + 2)²] . du A292 N POCO X2

AzY2 - 1 / ( Cosca) + 2) Cos(x) +2) da from table, entegration 2 [ (cos(x) +2) Jaux = 12.44799 in? - 2 3 .. A₂Y2 12.44799 inch AzY3 (7x0.52) (2.2) AY 1.7278 inch² 2 A = (4x2.2) 8.8 inch 2 2 Az = - 2 1 (cos(x) + 2) dx 9.81859 inch (from table) Tx0.5² - 0.7854 inch ² Az = Ay+ A₂Y₂ AY TE Ait A₂ - A3 9.68 + 12.44799 - 1-7278 8.8 + 9.81859 - 0.7894 Ý = 1.144 inch.

X - Aix, + A₂ - AX3 A+ A₂-Az Ax = (2.2x4) (0) y y -0. A282= sta t x da Area da = y da. xtda 2 2. 2 Ax2 = x. (y dx).

- 2 2 AX2 2 = x (Cosca) +2) dx - 2 (from integration table x (Colx+2) dx (since it is symmetrical about y-axis). i.Az x2 = 0. A₃9₂ (IT x 0.5²) + (0) 20.

A, x, + A1 - A₂ X 3 X = A + A₂-A3 oto-O Ait A₂-A3 Since the cross section is Symmetrical about y-axis, x=0) Centroid is located on y-axis and y 1.44 inches. ž=0 - location of centriod Y = - 1.44 inches,

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