# multivariable calculus – approximating unbounded integral in higher dimension

In multivariable calculus, I usually encounter this: if $$f: mathbb{R}^n rightarrow mathbb{R}$$, we can define $$int_{mathbb{R^n}} f(x) dx = lim_{R rightarrow infty} int_{B(0,R)} f(x) dx$$ if this limit exists where $$B(0,R)$$ is the ball centered at $$0$$ of radius $$R$$. However, for the case $$n=1$$, this is not true: consider the function $$f(x)=x$$. We know that $$int_{mathbb{R}} x dx$$ is undefined, but $$lim_{R rightarrow infty} int_{B(0,R)} x dx = 0$$. Can anyone explain to me why?