Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.2 Length of a Plane Curve, #29 · Calculus · Applications of integrals

(important) The line … is close to a staircase of pieces that…

(important) The line $y = x$ is close to a staircase of pieces that go straight across or straight up. With 100 pieces of length $Δ x = 1/100$ or $Δ y = 1/100$ , find the length of carpet on the staircase. (The length of the $4 5^{\circ}$ line is $2$ . The staircase can be close when its length is not close.)

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.2 Length of a Plane Curve, #29

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