Math Problem Statement

Find the Riemann sum approximation of the double integral

D (6x − 9y) dA where D is the rectangle D = [0, 4] ✕ [1, 5]. Use a regular partition by dividing D into 16 equal size subrectangles and taking sample points at the center of each subrectangle.

Solution

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Math Problem Analysis

Mathematical Concepts

Riemann Sum
Double Integral
Partitioning
Multivariable Calculus

Formulas

Riemann Sum for Double Integral: ∑ f(x_i, y_j) ΔA
Δx = (b - a) / n
Δy = (d - c) / m

Theorems

Riemann Sum Approximation Theorem
Double Integration over Rectangular Regions

Suitable Grade Level

College Level Calculus (Calculus III or Multivariable Calculus)