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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.3 Summation versus Integration, #37 · Calculus · Integrals

The sum … equals ______

The sum $Δ x \sum_{j = 1}^{1/Δ x} \frac{f ( j Δ x ) - f (( j - 1 ) Δ x )}{Δ x}$ equals ______.
In the limit this becomes $\int_{0}^{1}______d x =______$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.3 Summation versus Integration, #37

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