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If a(0,0,0) and b(2,2,2) are points in coordinate space, how many paths are there from a to b that move from one lattice point to another in the positive x-,y- or z- direction?

Write the summation to estimate the area under the curve y = 1 + x2 from x = -1 to x = 2 using 3 rectangles and right endpoints

Urgentwhat is the area of the figure?