Use Stokes' Theorem to evaluate $\int$_C 11z dx + 11x dy + 11y dz over the triangle with vertices (1, 0, 0), (0, 1, 0), and (0, 0, 1) traversed in a counterclockwise manner. A) 16.5 B) 11 C) 22 D) 44 E) 1

Question

Quizplus · Accepted Answer

The curl of F is (1, 1, 1), and the normal vector to the triangle is (1, 1, 1). So, the flux of the curl of F through the triangle is 1 + 1 + 1 = 3. Since the triangle has area 1/2, the surface integral of F over the triangle is 3/2 = 1.5.

Use Stokes' Theorem to Evaluate ∫\int∫ C 11z Dx + 11x Dy + 11y Dz Over

Use Stokes' Theorem to Evaluate $\int$ _C 11z Dx + 11x Dy + 11y Dz Over