Find the Centre of gravity in the shape of the asteroid x^(2/3) –y^(2/3) = a^(2/3) represented in the first quadrant

## Question

## Question

Find the Centre of gravity in the shape of the asteroid x^(2/3) –y^(2/3) = a^(2/3) represented in the first quadrant

## Topic

Applications of Double Integrals and Triple Integrals

## Problems

- Find the area of ellipse x^2/a^2 +y^2/b^2 =1 by double integration
- Find by double integration the area enclosed by the curve r=a (1+cosθ) between θ=0 and θ=π
- Find the volume generated by the revolution of the Cardioids r=a(1+cos(theta)) about the initial line
- Find the volume bounded by the cylinder x^2+y^2=4 and the planes y+z=4, z=0
- Find the volume of the solid bounded by the planes x=0, y=0, z=0, x+y+z=1
- Find the centre of gravity of the triangular lamina bounded by the coordinate axes and the line x/a + y/b =1
- Find the Centre of gravity in the shape of the asteroid x^(2/3) –y^(2/3) = a^(2/3) represented in the first quadrant