Consider an infinitely thin flat plate with a $1$ m chord at an angle of attack of $10$ in a supersonic flow. The pressure and shear stress distributions on the upper and lower surfaces are given by $p_u=4{10}^4(x-1{)}^2+5\mathrm{.}4{10}^4,p_{\text{I}}=2{10}^4(x-1{)}^2+1\mathrm{.}73{10}^5,r_u=288x^{-0\mathrm{.}2},$ and $r_{\text{I}}=785x^{-0\mathrm{.}2},$ respectively, where $x$ is the distance from the leading edge in meters and $p$ and $$ are in newtons per square meter. Calculate the normal and axial forces, the lift and drag, moments about the leading edge, and moments about the quarter chord, all per unit span. Also, calculate the location of the center of pressure. $($Round axial force to the nearest whole number and other answers to two decimal places.$)$

The normal force is $q,{10}^{5}N.$

The axial force is $$

The lift is ${10}^{5}N.$ N$.$

The drag is ${10}^{4}N.$

The moment about the leading edge is ${10}^{4}Nm.$

The moment about the quarter chord is ${10}^4\frac{N}{m}.$

The location of the center of pressure is $$ m$.$