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Determine whether the integral is divergent or convergent: If it is convergent, evaluate it: If it diverges to infinity; state your answer as "00' (withou...

Question

Determine whether the integral is divergent or convergent: If it is convergent, evaluate it: If it diverges to infinity; state your answer as "00' (without the quotation marks) . If it diverges t0 negative infinity; state your answer as If it diverges without being infinity or negative infinity, state your answer as "DNE" .4dtQuestion Help: @videoSubmit Question

Determine whether the integral is divergent or convergent: If it is convergent, evaluate it: If it diverges to infinity; state your answer as "00' (without the quotation marks) . If it diverges t0 negative infinity; state your answer as If it diverges without being infinity or negative infinity, state your answer as "DNE" . 4dt Question Help: @video Submit Question



Answers

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. $$ \int_{-\infty}^{0} e^{-x} d x $$

So in this costume, first rewrite, the integral is the limit. Let's be goes to infinity. These you're eating the power of native actually Axe. And now we're gonna integrate, and we're gonna apply that even the power of negative a ax. The ax is you put a negative one of Ray either The power of negative X plus our constant See. So we end up with this. When we integrate, we end up with the negative limited. Just be goes to infinity of either the power negative eyes e j. So now we can use the fundamental theory of calculus from the hand of Got anything negative limit as he goes to infinity. You the power of negative B minus one. So when we evaluate this limit, this is equal to negative. Then it is the power of negative entity minus one, which is negative zero minus one, which is one that's the answer to this question.

So first we're gonna rewrite this inter goal so limit. So it's gonna be a limit. Is a goes to negative infinity of this, you know? Zero. Okay. And the d s over next square plus one. This we just got from Mark Original given problem. So now we're gonna use our first we're gonna integrate, and we're gonna make this into the limit. Is a goes to need of infinity? Uh, yeah, you're I feel we're gonna change this now to inverse Han bash and then zero. So now in this new page will use the fundamental of calculus, which basically gets us to the limit as a goes to negative infinity of inverse fan of zero. Who's your mind next? Tan in verse of a which is just gonna be negative the minute that goes to negative infinity of inverse. So now that we're here, we can evaluate the limit and we get the negative. The inverse fan Negative infinity, which is gonna be pi over too. So the answer this question just gonna be the indigo would converge to pie or two

In the problem, since one of the integration is minus infinity. Therefore we have the integral is an improper integral. Now This is written as integration minus infinity to zero except on X squared plus one day X. So this is written as a limit attending to minus infinity one upon to integration 8-0 DT upon T Or we have excess choir plus one SD. This is twice of X dx. Nettie poster DT. This is written as limit, attending to minus infinity half limit model T 8-0, Softer putting the limits, we have this as infinity. Therefore it never says this is the answer.

In the problem, since one of the limit is infinitely, therefore it is an improper integral. The second part is we have to find whether it have a resort converses so we can write this limited limit, be tending to infinity. It would be, It's about X upon three the X. This is organized limit between into infinity degrees and 0 to be If the power x upon three d. x. This is recognized limit be turning to infinity Today. eight power x upon three, putting the limousine, A and B. Hence it is equal to three ft, the power x upon three minus three. So this is Infinity -3. This is equal to infinity. So we can say that this devil gauge, so this is our answer.


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