Evaluate the bounds of the x and y-coordinates to define the limits of the area of the region occupied by a specific lamina. If either the x or y bound involve a function, use it as your inner bound and use the constant values of the other as your outer bound. If both x and y limits are constants, the order of bounds is irrelevant.
Multiply the given density at the point (x,y) on the lamina by the distance of the point (x,y) from the y-axis. Set-up a double integral using the density multiplied by the y-coordinate as the function to be integrated and the area using the respective x and y-coordinates as the limitation bounds.
Integrate the function once by taking its anti-derivative and solving for the inner bound limits. Solve by integrating the function again by taking its anti-derivative and solving for the outer bound limits.
Evaluate the bounds of the x and y-coordinates to define the limits of the area of the region occupied by a specific lamina. If either the x or y bound involve a function, use it as your inner bound and use the constant values of the other as your outer bound. If both x and y limits are constants, the order of bounds is irrelevant.
Multiply the given density at the point (x,y) on the lamina by the distance of the point (x,y) from the x-axis. Set-up a double integral using the density multiplied by the x-coordinate as the function to be integrated and the area using the respective x and y-coordinates as the limitation bounds.
Integrate the function once by taking its anti-derivative and solving for the inner bound limits. Solve by integrating the function again by taking its anti-derivative and solving for the outer bound limits.