Vault Of Euclid

Flux of a Vector Field Across a Line Segment

Multivariable calculus warmup

Calculate the flux of \(\mathbf{F}=\langle x+y, 2y\rangle\) across the line segment from \((0, 0)\) to \((2, 3)\), where the curve is oriented from left to right.
calculusvector-calculusmultivariable-calculusline-integralfluxvector-fieldparametrizationline-segment2d-fluxevaluate-integralintegrationparametric-equations

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

What this problem tests

Tests the ability to parametrize a line segment, set up a 2D flux integral using the standard normal vector, and evaluate the resulting definite integral.

This problem is typical of an introductory vector calculus course, testing the basic setup and evaluation of a 2D flux integral.

More on Multivariable calculus

← today's set