# Thread: help with basic integral problem?

1. ## help with basic integral problem?

$\displaystyle \int_{-5}^5 \frac{2}{x^3} dx$

the answer i got is 0.

the answer in the back of the book says: Does not exist

what did i do incorrectly?

This is what I did: $\displaystyle \int_{-5}^5 \frac{2}{x^3} dx$
= $\displaystyle \frac{-1}{x^2}|_{-5}^5$
=$\displaystyle \frac{-1}{(5)^2}-(\frac{-1}{(-5)^2})$
=$\displaystyle \frac{-1}{25}+\frac{1}{25}$
=0

2. Originally Posted by yoman360
$\displaystyle \int_{-5}^5 \frac{2}{x^3} dx$

the answer i got is 0.

the answer in the back of the book says: Does not exist

what did i do incorrectly?
Note* this post will be updated soon so i can show you my work
The update will be unnecessary since you probably neglected to recognise it as an improper integral (the integrand is undefined at x = 0 which lies in the interval of integration). The first step is therefore to write:

$\displaystyle \lim_{\alpha \rightarrow 0} \int_{-5}^{\alpha}\frac{2}{x^3} \, dx + \lim_{\beta \rightarrow 0} \int_{\beta}^{5}\frac{2}{x^3} \, dx$.

(A pre-emptive) by the way, statements like $\displaystyle \infty - \infty$ make no sense and certainly do not equal zero ....

3. Originally Posted by mr fantastic
The update will be unnecessary since you probably neglected to recognise it as an improper integral (the integrand is undefined at x = 0 which lies in the interval of integration). The first step is therefore to write:

$\displaystyle \lim_{\alpha \rightarrow 0} \int_{-5}^{\alpha}\frac{2}{x^3} \, dx + \lim_{\beta \rightarrow 0} \int_{\beta}^{5}\frac{2}{x^3} \, dx$.

(A pre-emptive) by the way, statements like $\displaystyle \infty - \infty$ make no sense and certainly do not equal zero ....
ah i see since f is not continuous on [a,b] I can't use the fundamental theorem of calculus:
$\displaystyle \int_a^b f(x)dx=F(b)-F(a)$

where F is any antiderivative of f, that is, a function such that F'=f

Thank you so much for pointing that out I just forgot to check if its continuous on [-5,5] since its discontinuous at x=0 the integral does not exist