Divergence of the vector field $$$\overrightarrow V\left(x,y,z\right)=-\left(x\cos xy\;+\;y\right)\;\widehat i\;+\;\left(y\cos xy\right)\;\widehat j\;+\;\left(\sin\;z^2\;+\;x^2\;+\;y^2\right)\widehat k$$$ is

Divergence of the vector field $$v\left( {x,y,z} \right) = - \left( {x\,\cos xy + y} \right)\widehat i + \left( {y\,\cos xy} \right)\widehat j + \left[ {\left( {\sin {z^2}} \right) + {x^2} + {y^2}} \right]\widehat k\,\,$$

Consider the function $$f\left( x \right) = {\left( {{x^2} - 4} \right)^2}$$ where $$x$$ is a real number. Then the function has

The integral $$\,\,{1 \over {2\pi }}\int\limits_0^{2\Pi } {Sin\left( {t - \tau } \right)\cos \tau \,d\tau \,\,\,} $$ equals