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### Section 4-1 : Double Integrals

1. Use the Midpoint Rule to estimate the volume under $$f\left( {x,y} \right) = {x^2} + y$$ and above the rectangle given by $$- 1 \le x \le 3$$, $$0 \le y \le 4$$ in the $$xy$$-plane. Use 4 subdivisions in the $$x$$ direction and 2 subdivisions in the $$y$$ direction. Solution