Math Help - Improper integrals

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.