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Omni-MATH / Consider the paths from (0,0) to (6,3) that only take steps of unit length up and right. Compute the sum of the areas bounded by the path, the x-axis, and the line x=6 over all suc…

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problem

Consider the paths from (0,0)(0,0) to (6,3)(6,3) that only take steps of unit length up and right. Compute the sum of the areas bounded by the path, the xx-axis, and the line x=6x=6 over all such paths.
Plain-text mathematical notation (without MathML)
Consider the paths from (0,0) to (6,3) that only take steps of unit length up and right. Compute the sum of the areas bounded by the path, the x-axis, and the line x=6 over all such paths.
Original LaTeX notation
Consider the paths from \((0,0)\) to \((6,3)\) that only take steps of unit length up and right. Compute the sum of the areas bounded by the path, the \(x\)-axis, and the line \(x=6\) over all such paths.

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