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Numerade Educator



Problem 36 Hard Difficulty

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

$ \displaystyle \int_0^4 \frac{dx}{x^2 - x - 2} $


$-\infty,$ Divergent


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Video Transcript

the problem is determine whether each Negro it's ca mordant world that wouldn't you know it. They thought that a word it we could write it this integral as Jiro from there to four. Yeah, over X minus two. Last one. Things one acts goes to two. Denominated goes to zero. This is proper integral a definition. This is the Goto the girl found zero to two the axe over X minus two on DH X plus one us integral from two to four. Yes, over X minus two hands one No, we computed this integral forest. But this improper into girl by definition, this's recall to limit a goes to two from left side and integral from zero to a we can't write dysfunction. That's one third times one over X minus two, minus one over X Swan. Yes. Now look at this. Definitely to grow this deafening hero Eco's one third. Oh, and after a while, you x minus two, my ass. Yeah, And express long from zero to a and this is equal to one third you on X minus two over. Ex us long? Absolutely. You from zero to a No, Andi, Since these pico to one third ln a minus two over a plus one through the wind minus on Plotting zero. Here is this the trail and two What a goes to true from last night Side a minus two Over a plus Juan goes to infinity. I saw it goes to zero. So, Ellen, a man is to over a plus one goes to negative infinity. So dysfunction goes to negative infinity when a goes to two So this integral is tavern and