2013 RI P1 Q12

Find \(\displaystyle\displaystyle \displaystyle\int{\frac{9}{\sqrt{3+2x-{{x}^{2}}}}}\mathrm{ d}x\). Hence, find the exact value of the constant \(a\) for which \(\displaystyle\displaystyle \displaystyle\int_{\ 0}^{\ 2}{\frac{9}{\sqrt{3+2x-{{x}^{2}}}}\mathrm{ d}x=\displaystyle\displaystyle \displaystyle\int_{\ -\tfrac{1}{2}}^{\ a}{\pi \left| \,1-2x\, \right|}}\mathrm{ d}x.\)[7]