Question: Fundamental Theorem of Calculus:
We already have a definition of [a,b], it it makes no sense if the interval is opened (has to be closed). How would you go about saying that it has to be on a closed interval?

Question

amistre64 · Answer

i dont think it has to be restricted to a closed interval; hence, improper integrals

amistre64 · Answer

$$\int_{0}^{\infty}tan^{-1}(x)dx$$

anonymous · Answer

so it doesn't have to be on a closed interval? hmmm... makes sense

amistre64 · Answer

it is useful on a closed interval thats fer sure; but "need to be"? nah

amistre64 · Answer

i think I got my example wrong, but the premise is still the same ;)

anonymous · Answer

do you have a better example? :)

amistre64 · Answer

sure $$\int_{1}^{\infty}\frac{1}{x^2}dx=1$$ http://www.wolframalpha.com/input/?i=integrate+%281+to+infinity%29+1%2Fx%5E2

anonymous · Answer

Thank YOU!!

amistre64 · Answer

youre welcome