geerky42 one year ago Is it me or whoever answered my question makes no sense? http://www.peeranswer.com/study/mathematics/557e2b603102d10905d35bd5 My question:

1. geerky42

There is this property that states that $\int_k^kf(x)~\mathrm dx = 0\quad \forall~ k\in\mathbb R$ From what I understand, integral is area enclosed by $$f(x)$$ and x-axis. So this property makes sense since $$0\cdot f(k)=0$$, given that width of line is $$0$$. So saying we have $$f(x)=\dfrac{1}{x}$$, is $$\displaystyle \int_0^0 f(x)~\mathrm dx$$ still $$0$$? Because $$f(x)$$ doesn't exist at $$x=0$$ hence integral doesn't exist since it is basically $$0\cdot\text{indetermine}$$ So I believe property is supposed to be $\int_k^kf(x)~\mathrm dx = \begin{cases}0 & \text{if }~f(k)~\exists\\\not\exists & \text{if }~f(k)~\not\exists \end{cases}$ Right? If not, why not?

2. geerky42

@freckles @SithsAndGiggles