💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

WZ

# Determine whether each integral is convergent or divergent. Evaluate those that are convergent.$\displaystyle \int_0^\infty \frac{x^2}{\sqrt{1 + x^3}}\ dx$

## $\infty$, Divergent

#### Topics

Integration Techniques

### Discussion

You must be signed in to discuss.
##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp

### Video Transcript

the problem is determine whether this into grow is convergent or that wouldn't before with self this integral the first we can use you substitution toe compared this function function that easier twenty grow we can write you. If he called to one plus Act two Reese power then you if Iko too three ham's too square the axe you then this anti girl is ICO too So x squired d x This part is equal to one third you This is one over you to half on DH hams one third do you on one acts goes to zero you cause to want what axe goes to Bennett e You also goes to infinity the cost of energy and then use the definition of improper integral this ego to limit he goes tio financially on DH integral one third ham's one over are we could right dysfunction as you and Teo negative one half from one to and then find it's anti derivative Off this function, this is you cut to the limit, he goes to infinity and this is a constant number one third and aunt derogative of you to make you one half. This is E Coto one over. Negative one. Have Ruslan. How's you? You make it one half a swan from one to then planted in key and one here. So this is you. Coach is limited. He goes to infinity one third times. This is the one over one half. This's two ham's You to one half from one to on three Lim. He goes to infinity, my third to third hams he to one half minus one. The thing's monte goes to infinity. He to one half goes to infinity. So the answer is infinity. That's indeed, girl, that merchant.

WZ

#### Topics

Integration Techniques

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp