Applications of Double Integrals and Triple Integrals
With the knowledge of double and triple integrals, we can find Area, Volume and Centre of gravity of different objects.
Formula to find Area and Volume
Formula to find the Centre of gravity
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