• Stewart

  Calculate the mass and the center of mass of the triangular lamina with vertices located at \((0,0)\) and \((1,0)\) and \((0,2)\) in the \(xy\)-plane having a density function \(\rho(x,y) = 1+3x+y.\)

• Stewart

  On a semi-circular lamina, suppose the density at any point is proportional to the distance from that point to the circle’s center. What are the coordinates of the lamina’s center of mass?

• Stewart

  Calculate the moments of inertia about the \(x\)-axis, about the \(y\)-axis, and about the origin, of a unit disk centered at the origin with radius \(r\) and uniform density \(\rho.\)

• Stewart

  Calculate the surface area of the portion of the surface \(z=x^2+2y+2\) that lies above the triangular region in the \(xy\)-plane with vertices \((0,0)\) and \((1,0)\) and \((1,1).\)

• Stewart

  Calculate the surface area of the portion of the paraboloid \(z=x^2+y^2\) that lies under the plane \(z=9.\)