Centroid by Multivariate Integration: Applications

Finding the centroid by multivariate Integration:

Example 1:

Use integration to find the centroid of the plane lamina occupying the region shown (uniform density).

Image of a centroid

Solution 1

View the solution of example 1

Example 2:

Use integration to find the centroid of the plane lamina occupying the region shown (uniform density).

Image of a centroid

Solution 2

View the solution of example 2

Example 3:

Find the x-component of the centroid of the plane lamina in the region
bounded by the curve y = x2 and the lines y=1 and x=0, and has mass
per unit area p(x,y)=x+y

Solution 3

View the solution of example 3

Example 4:

Use the composite region method to find the centroid of the blue shaded region in the figure:
Image of a centroid

Solution 4

View the solution of example 4

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