Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §14.1 Double Integrals, #45 · Multivariable Calculus · Multiple integrals

… might not approach … if we only know that

$\sum y_{i} Δ A$ might not approach $\iint y d A$ if we only know that $Δ A \to 0$ . In the square $0 \leq x, y \leq 1$ , take rectangles of sides $Δ x$ and $1$ (not $Δ x$ and $Δ y$ ). If $(x_{i}, y_{i})$ is a point in the rectangle where $y_{i} = 1$ , then $\sum y_{i} Δ A =$ ______. But $\iint y d A =$ ______.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.1 Double Integrals, #45

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