1. ## Improper integrals

can someone please explain to me step by step what I am supposed to do? I'm very confused at the moment. thanks for any help.

Evaluate the integral:
the integral from 1 to infinity of dx/(x^1.001)

2. Originally Posted by turtle
can someone please explain to me step by step what I am supposed to do? I'm very confused at the moment. thanks for any help.

Evaluate the integral:
the integral from 1 to infinity of dx/(x^1.001)

$\displaystyle \int_1^{\infty}\frac{1}{x^{1.001}}dx$

which by the standard rules for the integral of a power other than -1:

$\displaystyle \int_1^{\infty}\frac{1}{x^{1.001}}dx=\left[ -\frac{1}{0.001}\,\frac{1}{x^{0.001}}\right]_1^{\infty}=1000$

RonL

3. Originally Posted by turtle
can someone please explain to me step by step what I am supposed to do? I'm very confused at the moment. thanks for any help.

Evaluate the integral:
the integral from 1 to infinity of dx/(x^1.001)
$is integral$ x^-1.001 dx = x^-0.001/0.001 should apply limit

= (1^-0.001/0.001) - (1/infinite)
= 1/0.001 - 0
= 1000