English: Using only the fundamental theorem of calculus in one dimension, students can verify the divergence theorem by direct integration. The result is that ${\displaystyle \int _{\mathsf {V}}\left(\mathbf {\vec {\nabla }} \cdot \mathbf {\vec {F}} \right)\,dV}$ equals ${\displaystyle \oint _{\mathsf {S}}\left(\mathbf {\vec {F}} \cdot \mathbf {\hat {n}} \right)\,dS}$ equals ${\displaystyle \left(F_{x}(x_{2})-F_{x}(x_{1})\right)\cdot A.}$ The result is rectricted to the special case of the rectangular box shown, with the vector field of the form, ${\displaystyle \mathbf {\vec {F}} =F_{x}(x)\mathbf {\hat {i}} +F_{y}(x)\mathbf {\hat {j}} }$ where ${\displaystyle (F_{x},F_{y})}$ are arbitrary (but sufficiently "nice") functions of ${\displaystyle x.}$