$(8$ pts$)$ Determine by integration the centroid $(\stackrel{}{x},y)$

of the shape in the figure $($to the right$).$ ALL STEPS

must be shown.

a$.$ Showing the SLICE and dimensioning

b$.$ Calculation of height and length of slice

i$.$ Height $=y_{\text{F}\text{I}\text{N}\text{A}\text{L}}-y_{\text{I}\text{N}\text{I}\text{T}\text{I}\text{A}\text{L}}$

ii$.$ Length $=x_{\text{F}\text{I}\text{N}\text{A}\text{L}}-x_{\text{I}\text{N}\text{I}\text{T}\text{I}\text{A}\text{L}}$

c$.$ Calculation of AREA.

d$.$ Calculation of the $1^{st}$ moment area

e$.$ Calculation centroid location