Exercise 1905Calculus › Multivariable calculus › Vector calculusL1Added 3 Nov 2026

Flux through a cube

#divergence#cube#flux

Statement

Compute the outward flux of $\vec F=(x^2,0,0)$ through the cube $[0,1]^3$ .

Hint

$\operatorname{div}\vec F=2x$ ; integrate over the cube.

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Divergence. $\operatorname{div}\vec F=2x$ .

Integral. $\iiint_{[0,1]^3}2x\,dV=2\cdot\frac12=\frac12\cdot1=1$ .

Conclusion. Flux $=1$ .