1. ## Improper integrals

Hey guys I'm having a little trouble with improper integrals in general and I came here looking for some help. I need to know which integrals are convergent and divergent and which integrals are improper.

Can someone give me a couple points and tips when dealing with improper integrals.

An example problem is x^4 e^-x^4 dx l infinity and 1

2. ## Re: Improper integrals

Originally Posted by kashmoneyrecord3
Hey guys I'm having a little trouble with improper integrals in general and I came here looking for some help. I need to know which integrals are convergent and divergent and which integrals are improper.

Can someone give me a couple points and tips when dealing with improper integrals.

An example problem is x^4 e^-x^4 dx l infinity and 1

Pauls Online Notes : Calculus II - Improper Integrals

for your specific example, start by noting the following inequality ...

$\int_1^\infty x^4 e^{-x^4} \, dx < \int_1^\infty 4x^7 e^{-x^4} \, dx$

for the larger integral, let $t = x^4$

$dt = 4x^3 \, dx$

substitute ...

$\int_1^\infty t e^{-t} \, dt$

using integration by parts, it's a fairly simple process to show the convergence of this integral.

since the improper integral in question is less than this convergent improper integral, by direct comparison they both converge.

3. ## Re: Improper integrals

Originally Posted by kashmoneyrecord3
Hey guys I'm having a little trouble with improper integrals in general and I came here looking for some help. I need to know which integrals are convergent and divergent and which integrals are improper.

Can someone give me a couple points and tips when dealing with improper integrals.

An example problem is x^4 e^-x^4 dx l infinity and 1
Find a textbook with lots of examples. Your institute's library will have shelves of relevant books. Use a search like Google. Ask your teacher. etc.