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WZ
Numerade Educator

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Problem 10 Medium Difficulty

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

$ \displaystyle \int_{-\infty}^0 2^r\ dr $

Answer

converges to $\frac{1}{\ln 2}$

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Video Transcript

the problem is determined. Why that this into girl? It's too burdened or dumber. Didn't we felt we find the integral? What's this function? First we need to find anti derogative. I was a function to to ask power. So let's say how to find it and iterative with dysfunction. So true to ask power the virility of dysfunction. Is he going to go out? And Teo Ham's You too as power. So wanderer Allen too hams to to ask power. They were the relative or dysfunction. It is equal to one over Allen too. Ham's Alan too, to us power. This is the ICO too. Two as power. So Aunt had derivative. It was a function to us power. It's equal to one over our and two hams to to ask power. Then we used the definition of improper Integral Sir, this anti girl as equal to limit. Hey goes to negative infinity on an integral off you two Ask power Yaar and he Frankie too. Zero! This is a culture of limit. Teo, Mick, Give infinity on DH and a derivative with dysfunctions that this is one over our end. Two hams to to ask power from he to zero and then plug inch hero. And he too Dysfunction. This is the coach is the limit. He goes to negative infinity wand over how? In two hams. Two to zero. This one minus to to he Thanks. Won t goes to negative infinity to to kiss power goes to zero So the answer should be won over How? In two So this integral is converted on its volume is one over I went to