Potential Functions: Find a potential function for each vector field.

uncaught exception: Http Error #500

in file: /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 68
#0 /var/www/html/integration/lib/php/Boot.class.php(769): com_wiris_plugin_impl_HttpImpl_1(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Http Error #500') #1 /var/www/html/integration/lib/haxe/Http.class.php(532): _hx_lambda->execute('Http Error #500') #2 /var/www/html/integration/lib/php/Boot.class.php(769): haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Http Error #500') #3 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(30): _hx_lambda->execute('Http Error #500') #4 /var/www/html/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Http Error #500') #5 /var/www/html/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), Object(sys_net_Socket), NULL) #6 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(43): haxe_Http->request(true) #7 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(268): com_wiris_plugin_impl_HttpImpl->request(true) #8 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(307): com_wiris_plugin_impl_RenderImpl->showImage('fe8bce59e4439e5...', NULL, Object(PhpParamsProvider)) #9 /var/www/html/integration/createimage.php(17): com_wiris_plugin_impl_RenderImpl->createImage('

Step by step solution

01

Step 1. Given Information.

The vector field is

02

Step 2. Calculation.

The potential function is given by $g\left(x,y,z\right)=\int xdx+B+C$

Where, Here, B is integral with respect to y of the terms in which the x does not appear, and C is integral with respect to z of the terms in which the x and y does not appear.

So,

$\int 2x{y}^{2}z{e}^{x^{2}yz}dx=y{e}^{x^{2}yz}+\beta$

and $B=0$, $C=0$.

Potential function is$g(x,y,z)=y{e}^{x^{2}yz}$

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