Use integration to find the center of mass of the rectangle (1,-3) (4,-3) (4,5) (1,5).

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The center of mass of the rectangle (1,-3) (4,-3) (4,5) (1,5) has to be determined.

The diagram of the rectangle is:

The coordinates of the center of mass of the rectangle is given by:

`M_x = (int_1^4 x(5 - (-3)) dx)/(int_1^4 (5 + 3) dx)`

= `(8x^2/2)_1^4/((8x)_1^4)`

=>`(4*16 - 4*1)/(32 - 8)`

=> `60/24`

= `5/2`

`M_y = (int_1^4 (1/2)(25 - 1) dx)/(int_1^4 (5 + 3) dx)`

= `(12x)_1^4/24`

= `36/24`

= `3/2`

The center of mass of the rectangle is (2.5, 1.5)

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