Find exact areas and assess numerical integration results
Use radians and natural logarithms. Keep exact values unless a rounding instruction is stated
\[f(x)=\frac{-1}{\sqrt{9-(x+1)^2}},\qquad -\frac{5}{2}\le x\le \frac{1}{2}\]
Find the signed integral I and the geometric area A between the curve and the x-axis on this interval. Enter their coefficients Ipi and Api in
\[I=I_{\pi}\pi,\qquad A=A_{\pi}\pi\]