Question

Evaluate the following improper integral and state if the integral converges or diverges; definite integral dx/(x+2)^3, upper infinty, lower 0

Answer 1

someone pls help! sos

Answer 2

\[\large \int\limits_0^{\infty}\frac{dx}{(x+2)^3}\]So just taking the integral, ignoring the limits for now... were you able to do that part? Find the anti-derivative of the function?

Answer 3

ok...

Answer 4

That was a question....

Answer 5

um, no i wasn't

Answer 6

Ok let's rewrite it using rules of exponents :) Maybe that will help.
\[\large \int\limits \frac{dx}{(x+2)^3} \qquad = \qquad \int\limits\frac{1}{(x+2)^3}dx \qquad = \qquad \int\limits (x+2)^{-3}dx\]
Understand what I did there?
I haven't done the integration yet, but rewriting it like this will allow us to apply the power rule for integrals.

Answer 7

ya...

Answer 8

perfectly

Answer 9

From here just apply the power rule! :D\[\large \int\limits x^n \;dx =\frac{1}{n+1}x^{n+1}\]Remember that?

Answer 10

\[\large \int\limits (x+2)^{-3}dx \qquad = \qquad \frac{1}{-3+1}(x+2)^{-3+1}\]

Answer 11

um, so...?