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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.1 The Idea of the Integral, #15 · Calculus · Integrals

(Important) Let … be the area under the … curve, above the…

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(Important) Let $f (x)$ be the area under the $x$ curve, above the interval from $0$ to $x$ . The area to $x + Δ x$ is $f (x + Δ x)$ . The extra area is $Δ f =$ ____. This is almost a rectangle with base ____ and height $x$ . So $Δ f /Δ x$ is close to ____. As $Δ x \to 0$ we suspect that $df / d x =$ ____.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.1 The Idea of the Integral, #15

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