Question

also need actual moment of inertia answer. Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x=4y-3y² and the line x+5y=0 if δ(x, y)=x+5y. Select the order of integration th

Answer 1

To find the moment of inertia about the x-axis of a thin plate bounded by a parabola and a line, we need to integrate the product of the mass density function and the square of the distance between the infinitesimal mass element and the x-axis.

Step-by-step explanation:

To find the moment of inertia about the x-axis of the given thin plate bounded by the parabola x=4y-3y² and the line x+5y=0, we need to integrate the product of the surface density function and the square of the distance between the infinitesimal mass element and the x-axis.

Let's define the mass density function as δ(x, y) = x+5y. Solving the equations x=4y-3y² and x+5y=0, we find the limits of integration as y=0 and y=4/9.

Integrating the product of δ(x, y) and (x²+y²) with respect to x and y, and using the given limits of integration, we can calculate the moment of inertia about the x-axis of the thin plate.