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

WZ

# Find the value of the constant $C$ for which the integral$$\displaystyle \int_0^\infty \left (\frac{1}{\sqrt{x^2 + 4}} - \frac{C}{x + 2} \right)\ dx$$converges. Evaluate the integral for this value of $C$.

## If $C<1, L=\infty$ and $I$ diverges.If $C=1, L=2$ and $I$ converges to $\ln 2+\ln 2^{\circ}=\ln 2$If $C>1, L=0$ and $I$ diverges to $-\infty$

#### Topics

Integration Techniques

### Discussion

You must be signed in to discuss.

Lectures

Join Bootcamp

### Video Transcript

the problem is finding a wire you off the cast in the sea for wage into euro. This one converters. Your planet is integral for this. Funny. All the same with this problem. First we compute integral off one over you, Teo. I'm square us for Yes. Well, come here indefinitely into girl. This one? Yeah. We use U substitution. But you is equal to two towns hand. And this beta Then do you is ICO too? You think and square he's And this function is this definite indeed. Grow as we got you in definite integral one over. You're tough. Oh, and in the square ums to think and center square this is denominator is four times and played square Past wants this is equal to. And you girl Oh one over. Shoot hams, steak and this leader two times in a square. Is it here? We use the identity one class kind. The square is equal to They can see it is quiet. We use this identity Now This anti girl is this integral is in the grow off second data. These this is Nico too, you know, and absolutely off tannins. Hey, the last second things were a lot of you. Is ICO too hand in the CIA. And now so will That axe is equal to tannin data now, tenancy there is Axe and Buzz, and then they want last canons. Glad is equal to second, Claire. They can't see. That is You Goto one plus x square. So this is one class, I swear. What if this one is the culture? Say can? Yeah, his answer is, is equal to L. A. And this is X. Russ, You know one class now we're here. We read acts. Is he going to two hands? Ten minutes a day. So? So here, this is I square away for and yeah, this is square four through this one. This's answer. Was that indefinitely? Integral. Off indefinitely. Integral. Off. One over. No, my style. Us for the ex as equal. This is going to end. Act us? No. Plus X squared over four. Awesome, constant number. See? Yeah. Now for the integral. From there to infinity. One over X squared plus four minus. See over. Exposed to the ice. So first party is you go to. So this issue going to integral from there between Vanity one over. I'm square plus or uh, yes. And, um anyway, can Right here. So we kind of like this is that you go to that definition has a limit. It goes to infinity Mitt of zero to a of this function. Yeah, that's his functions At LAX X no is equal to its limit. A goes to infinity from a one over X squared plus or the on minus integral from their own toe. A C over X plus two the ex. And this is legal to the limit. It goes toe vanity, we have computer Tio, this swallow is yuko too X plus you're a tough one for us. I'm square four from zero to a and this car minus. This's out. I just So the council members see from zero to a we can write. This is equal to later. Just to infinity on ex us. New tough one class destroyer for over This is Xcor. Thanks. Plus two Teo thiss power problem, you know? Sure. Yeah, No, this is called to the limit from a goes to infinity. Oh, and X plus No one class ex Claire, this is That's a plus two to seize power, there is a this is equal to club buying. A and zero here says You got to claim it. It goes toe infinity out on a class one of us a squared away for over a plus two to save power minus. So as for the cereals, this is on one over on one of us. Oh yes, one over to this hour. Now look has this part. When they goes to infinity a plus you till this one over a plus. Choose to cease power. So you say's You kowtow, Juan. Say, is it you want? It's a plus beautif one clasp a square or for over a plus two. A girl goes to a cast, and the number this part will be a constant number. Just located a degree of a for the denominator. Numerator is the same on If Sae's not equal Juan for them to say and smart, it's great is a while. Then this number goes to zero, so L and zero goes to infinity. The limit does not exist. You say it's more than one disfunction goes to infinity and now any vanity goes to infinity limit Also this now that you confessed so why I will say is one Say, if you want Lim off, this one is equal to say. Is it once a cynical to l A and one of us? Joe? When divided A for both sides on a one over a story to us one. Or listen, I want us to oversee over a want a goes to infinity. Is this coastal zero? This is zero to zero. This is our end one. That's why I feel this oneness. Ellen, I want us motive one over fourth, class one and minus. Oh, and one half. This is Ellen three over two minus. When? This hour No, we write Tio. Yes. Three. Over to minus one. Have. This is a culture out and three. This is so why there?

WZ

#### Topics

Integration Techniques

Lectures

Join Bootcamp