Closed Integral Dx 4E2378

1. **Stating the problem:** We need to evaluate the integral $$\oint dx$$. 2. **Understanding the integral:** The symbol $$\oint$$ denotes a closed line integral, typically over a closed curve. 3. **Integral of $$dx$$:** The integral $$\oint dx$$ means integrating the differential $$dx$$ over a closed path. 4. **Key rule:** Since $$dx$$ represents an infinitesimal change in $$x$$, integrating $$dx$$ over any closed path returns to the starting point, so the net change in $$x$$ is zero. 5. **Therefore:** $$\oint dx = 0$$ 6. **Explanation:** The integral of $$dx$$ over a closed loop sums all the small changes in $$x$$ around the loop. Because the path is closed, the starting and ending points are the same, so the total change in $$x$$ is zero. **Final answer:** $$\boxed{0}$$