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2. Consider the following questions related to polar coordinates and geometric integrals. (a) Find the centre of the circle \( r=3 \sin \theta-4 \cos \theta \), and write the answer in Cartesian coordinates [ 5 marks] (b) Sketch the two curves \( r=-3 / \sin \theta \) and \( r=4(1-\sin \theta) \). Find the smaller area of the region bounded by these two curves. \( [9 \) marks] (c) Find the length of the curve \( y=\frac{x^{2}}{2}-\frac{1}{4} \ln x \) for \( x \) in the range \( x=1 \) to \( x=2 \). [6 marks] [End of Question 2; 20 marks total]

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