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.

Form a partial differential equation by eliminating the arbitrary constants a,b,c from z = ax+by+cxy

Find a partial differential equation of all spheres of given radius.

Find the complete integral of               p+q = sin x + sin y

Expand sin x as a finite series in powers of x , with remainder in Lagrange's form. Hence find the series for sin x .

Using Maclaurin's series expand the following function in powers of x 

e^{sin x}

If xy = 4 , find the maximum and minimum value of 4x + 9y