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Problem 30 Hard Difficulty
Determine whether each integral is convergent or divergent. Evaluate those that are convergent.
$ \displaystyle \int_{-1}^2 \frac{x}{(x + 1)^2}\ dx $
Answer
Divergent
Topics
Integration Techniques
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Video Transcript
the problem is getting wider. Each integral is converted over skyward and wild about the tales that converted base one acts goes to next. One. Dysfunction. The denominator of dysfunction goes to zero. This's an improper, integral after mission. This is equal to Lim. A toast to make one from right hand side Andi into grow is a from a too two act's over past one squire the ex. So we computed the definite into zero first. But this definitely eating girl we can read. Write. It's a function X plus one over us. One squire, minus one over express one square The ice. Yeah. Then this's a yuko to Ellen. Ex us Juan from a too minus negative one over X paswan from a tutu, This is Echo Two, Ellen three minus. How in a cross want Andre? Here's this in class one third, minus one over a plus one. We can read like his dysfunction eyes How in three US one third, minus X plus one One here is a eh Right here a swan. How plus one A swan over a swan. Look at this function. When a goes to next to one a plus one goes to zero. It's a press want times how in a swan. But this dysfunction it goes to zero. So the whole function goes to infinity. So this interview is that word?
Topics
Integration Techniques
Top Calculus 2 / BC Educators
Anna Marie V.
Campbell University
Kayleah T.
Harvey Mudd College
Samuel H.
University of Nottingham
Joseph L.
Boston College
