Let $\vec{F}=\left(2+6 x e^{3\left(x^{2}+y^{2}\right)}\right) \vec{i}+\left(6 y e^{3\left(x^{2}+y^{2}\right)}\right) \vec{j}$ Use the curl test to check whether $\vec{F}$ is path-independent.
A)Path-independent
B)Not path-independent

Question

Quizplus · Accepted Answer

The curl of $\vec{F}$ is zero, indicating that $\vec{F}$ is conservative and thus path-independent.

Let F⃗=(2+6xe3(x2+y2))i⃗+(6ye3(x2+y2))j⃗\vec{F}=\left(2+6 x e^{3\left(x^{2}+y^{2}\right)}\right) \vec{i}+\left(6 y e^{3\left(x^{2}+y^{2}\right)}\right) \vec{j}F=(2+6xe3(x2+y2))i+(6ye3(x2+y2))j​ Use the Curl Test to Check Whether

Let $\vec{F}=\left(2+6 x e^{3\left(x^{2}+y^{2}\right)}\right) \vec{i}+\left(6 y e^{3\left(x^{2}+y^{2}\right)}\right) \vec{j}$ Use the Curl Test to Check Whether