`int_-3^0(1 + sqrt(9 - x^2))dx` Evaluate the integral by interpreting it in terms of areas.
Consider the graph of y=f(x)=`1+sqrt(9-x^2)`
This is the equation of circle of radius 3 centred at (0,1)
The integral can be interpreted as the area of a quarter of the said circle and the area of the rectangle whose vertices are (0,0),(0,1),(-3,1) and (-3,0).Plot can be seen in the attached graph.
We will use standard integral `intsqrt(a^2-x^2)dx=(xsqrt(a^2-x^2))/2+a^2/2arcsin(x/a)+C`