MediumIntegrals

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.7 The Fundamental Theorem and Its Applications, #32 · Calculus · Integrals

The four-dimensional cube … has hypervolume … ______

The four-dimensional cube $0 \leq x, y, z, t \leq s$ has hypervolume $H =$ ______. The face with $x = s$ is really a ______. Its volume is $V =$ ______. The total volume of the four faces with $x = s$ , $y = s$ , $z = s$ , or $t = s$ is ______. When $s$ is increased by $Δ s$ , the extra hypervolume is $Δ H \approx$ ______. So $d H / d s =$ ______.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.7 The Fundamental Theorem and Its Applications, #32

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