why does this integral not exist ∫-5 to 5 (10/(x^3))dx ? and this one ∫x to 2x -10csc^2(x) dx ?

Question

johnweldon1993 · Answer

Not exist? Well it does exist...

$$\large \int_{-5}^{5} \frac{10}{x^3}dx$$
$$\large 10\int_{-5}^{5} \frac{1}{x^3}dx$$
$$\large 10\int_{-5}^{5} x^{-3}dx$$

if you do that out...you do get a number...what do you get?

anonymous · Answer

well the computer says that's the correct answer so idk

amistre64 · Answer

how can you integrate across a domain that includes a value thats not in the domain?

amistre64 · Answer

0 is a bad value for dividing by

amistre64 · Answer

$$\int_{-5}^{5}10x^{-3}~dx=\lim_{t\to 0}\left(\int_{-5}^{t}10x^{-3}~dx+\int_{t}^{5}10x^{-3}~dx\right)$$

amistre64 · Answer

if the limit exists, then the integration is defined by it;  if it doesnt exist, then the integration does not converge

anonymous · Answer

thanks!