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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.5 The Definite Integral, #28 · Calculus · Integrals

Suppose … is a multistep function with jumps of … at the…

$W (x)$ equals 1 at $x = \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots$ , and elsewhere $W (x) = 0$ . For $Δ x = .01$ find the upper sum $S$ . Is $W (x)$ integrable?

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 $s .$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.5 The Definite Integral, #28

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