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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.1 The Idea of the Integral, #25 · Calculus · Integrals

From … to …, the area under … is

From $x$ to $x + Δ x$ , the area under $v = x^{2}$ is $Δ f$ . This is almost a rectangle with base $Δ x$ and height ____. So $Δ f /Δ x$ is close to ____. In the limit we find $df / d x = x^{2}$ and $f (x) =$ ____.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.1 The Idea of the Integral, #25

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