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Find the x and y coordinates of the centroid of the shape shown below via integration.

The image depicts a coordinate plane with a shaded trapezoidal shape. The trapezoid's dimensions are marked as follows:

- The height from the base to the top of the trapezoid is 10 inches.
- The top horizontal side of the trapezoid is 3 inches in length.
- The bottom horizontal side of the trapezoid extends 8 inches along the x-axis.
- The left side of the trapezoid is aligned with the y-axis.

The trapezoid slopes diagonally inward from the top left to the base, creating a geometric shape that reflects these specified dimensions on the coordinate plane.

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