The temperature distribution across a wall I $m$ thick at a certain instant of time is given as $T=a+bx+c{x}^{2}T$ is in degree celcius and $x$ is in meters. $a=900C,b=-300\frac{C}{m}.c=-50\frac{C}{m^2}.$ A uniform heat generation $q=1000\frac{W}{m^3}$ is present in the wall of area $10m^2$ having the properties $p=1600k\frac{g}{m^3}.K=40\frac{W}{m}.K$ and $Cp=4K\frac{j}{k}g.K.$

i$)$ Determine the rate of heat transfer entering the wall