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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