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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.1 The Idea of the Integral, #3 · Calculus · Integrals

The differences between … are

This problem is about sums $f_{j}$ and differences $v_{j}$ .

The differences between $f = 1, 1/2, 1/4, 1/8$ are $v = - 1/2, - 1/4, - 1/8$ . These negative $v$ 's do not add up to these positive $f$ 's. Verify that $v_{1} + v_{2} + v_{3} + v_{4} = f_{4} - f_{0}$ is still true.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.1 The Idea of the Integral, #3

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