Find the volume of sphere                    x² + y² + z² =  a² using triple integrals.

Find the volume bounded by xy- plane, the cylinder x²+y²= 1 and the plane       
x+y+z = 3

Find the volume in the positive octant bounded by the plane x+2y+3z =4 and the coordinate planes.

A circular hole of radius b is made centrally through a sphere of radius a . Find the volume of remaining sphere.

Find the centroid of the upper half of the circle x²+y²= a²

Find the area bounded between the curve y²= 4x and x²= 4y using Green's theorem.

Using Green's theorem in xy plane find the area of the region in the xy plane bounded by y³ = x² and y=x .

Find the area of a circle of radius a using Green's theorem.

Form the differential equation by eliminating a and b from y =a tan x + b sec x.

Express x⁵ in term of legendre polynomials.

Find the differential equation of all spheres whose centres lie on the Z-axis.