a. By using integral calculus, find the area of the region bounded by the graphs of y = x^2 and y = 4. (x and y are in meters.)
b. Consider with the shape with the area calculated in a). The area mass density (sigma=dm/dA) of this material is given by sigma(x, y) = 1 + 2y + 6x2. [in kg/m2]. Obtain the mass of this object.
c. Calculate the rotational inertia of this object when it is spinning around y-axis.
d. Calculate the rotational inertia of this object when it is spinning around x-axis.