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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.5 The Definite Integral, #30 · Calculus · Integrals

If … and … explain

Suppose $M (x)$ is a multistep function with jumps of $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots$ , at the points $x = \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots$ . Draw a rough graph with $M (0) = 0$ and $M (1) = 1$ . With $Δ x = \frac{1}{3}$ find $S$ and $s$ .

If $df / d x = - v (x)$ and $f (1) = 0,$ explain $f (x) = \int_{x}^{1} v (t) d t .$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.5 The Definite Integral, #30

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