Can anyone do these two area integrals?

Question

what is the value of the area integral int((r^2+1)dA) over the interior of the square with side 2 centred on the origin and parallel to the x and y axes. What would the value of this be for a circle of radius 2 centred on the origin?

Answer 1

r^2+3

Answer 2

since the domain of the first is a square

convert the integral to cartesian .. . . or rectangular

∫(-1,1) ∫(-1,1) (x^2 + y^2 + 1) dy dx

= ∫ [x^2y + y^3/3 + y] {from -1 to 1}  dx

= ∫ [2x^2 + 8/3] dx

= 2x^3/3 + 8x/3 .. . .. . x from -1 to 1

= 4/3 + 16/3

= 20/3

to solve the next

∫(0,2π) ∫(0,2) (r^2+1) r dr dθ

solve that ....