Please provide a detailed solution. Thanks! Density , thickness-t Figure P4.5 4.5 Th Figúre P4.5. Find, by integration: e midpla ne of a uniform triangular plate is shownin Jy c. 1 xy What would be good approximations were the plate thin? Solution 4.5 for the given planar triangle densoty = rho thickness = t hence a. dIxx = integrate(dm*y^2) dm = rho*t*dA = rho*t*dy*(B - By/H) hence dIxx = integrate(rho*tB(1 - y/H)y^2*dy) = rho*tB(y^3/3 - y^4/4H) from y = 0 to y = H Ixx = rho*tB(H^3/3 - h^4/4H) = rho*tB*H^3(1/3 - 1/4) = rho*t*B*H^3/12 b. from symmetry we can say dIyy = integrate(rho*t(Hx/B)x^2*dx) dIyy = rho*t*H*B^3/4 c. now, Izz = Ixx + Iyy hence Izz = rho*t*B*H(B^2/4 + H^2/12) d. dIxy = integrate(dm*xy) dIxy = integrate(rho*t*(Hx/B)x(Hx/B)dx) from x = 0 to x = B hence Ixy = rho*t*H^2B^2/4 e. dIxz = integrate(dm*xz) dIxz = integrate(rho*t*(Hx/B)xz*dx) now, this is an odd fucntion of z hence Ixz = 0 similiarly Iyz = 0 hence for thin plate Ixz = Iyz = 0 and rest equations remain the same .