Compare an arcsine integral with an absolute-value area

(a) Find the exact value of $\int_1^2x^2\ln x\,dx$.3 marks

(b) Find $\int9/\sqrt{3+2x-x^2}\,dx$. Hence find the exact constant $a$ satisfying

$$\int_0^2\frac9{\sqrt{3+2x-x^2}}\,dx=\int_{-1/2}^{a}\pi|1-2x|\,dx.$$