MediumVector calculus

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §15.2 Line Integrals, #26 · Multivariable Calculus · Vector calculus

(d)

Compute the work $W (x, y) = \int M d x + N d y$ on the straight line path $(x t, y t)$ from $t = 0$ to $t = 1$ . Test to see if $\partial W / \partial x = M$ and $\partial W / \partial y = N$ .

(a) $M = y^{3}, N = 3 x y^{2}$

(b) $M = x^{3}, N = 3 y x^{2}$

(c) $M = x / y, N = y / x$

(d) $M = e^{x + y}, N = e^{x + y}$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §15.2 Line Integrals, #26

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