Describe the term Kalpanaswaram.
Kalpanaswaram is an improvisational aspect of Carnatic music where the performer spontaneously creates sequences of swaras (musical notes) adhering to the rules of the raga and tala. It is typically performed after the main composition (kriti) to showcase the musician's creativity, knowledge, and mastery over melody and rhythm.
Key features of Kalpanaswaram include:
Kalpanaswaram is a vital and exciting feature of Carnatic concerts, offering an opportunity for creative exploration within strict classical frameworks.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).