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Numerade Educator



Problem 23 Medium Difficulty

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

$ \displaystyle \int_{-\infty}^0 \frac{z}{z^4 + 4}\ dz $


$-\frac{\pi}{8}$, Convergent


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Video Transcript

the problem is determined why the h Integral is convergent or divergent evaluated those that are converted. But this improper integral by definition this is equal to eliminate it. Hey, goes to negative Infinity, integral from 8 to 0 of function is the over 32 four plus two. The see we compute is definitely integral first. So for that this definitely integral First we can use use substitution that u is equal to Z square then see you D u is equal to choosy Dizzy Now we can read Write this definitely integral as integral Here this is from a square she's zero and this one half ew over you, Squire us or this is equal to one over one half times integral of a Squire zero of one over you square us two square You we know anti derivative of this function. It's act tenant you over two times one half This is the echo to one half um, one half, uh, tenant you over. So from Esquire 20 Yes, it's Echo two 1/4 acting and 00 So this is zero minus a tenant. Mhm a square over to we know when he goes to negative. Infinity A Squire over to goes to infinity. An act tenant a square over to goes to Hi, Laura two. So for this function improper, integral. This is equal to negative one force times high over to this Is the culture negative high over eight?