`int_0^1 int_1^2 (x^2+y^2) dx dy`

int_0^1 int_y^sqrt(y) (x^2+y^2) dy dx=

int_0^2 int_0^sqrt(4+x^2) (dx dy)/(4+x^2+y^2) =

int_0^1 int_0^sqrt(1+x^2) (dy dx)/(1+x^2+y^2)

int_0^1 (x+x^2)dx

int_0^1 x(1+x)^2*dx

int_0^1 x^2(1-x)^(3/2) dx=

int_0^1y^2sqrt(1-y^2)dy

(i) int_4^5 1dx (ii) int_-1^2 x dx (iii) int_0^4 x^(1//2) dx (iv) int_0^4 x^(3//2) dx (v) int_0^8 x^(5//3) dx

int int_(R)(x^(2)+y^(2))dxdyR:{(x,y):0<=x<=1,1<=y<=2}