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Georgia Southern University

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Problem 50

Use the region $R$ with the indicated boundaries to evaluate each double integral.

$$\iint_{R} \frac{1}{x} d y d x ; \quad 1 \leq x \leq 2,0 \leq y \leq x-1$$

Answer

$=[1-\ln 2]$

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## Discussion

## Video Transcript

Okay, so here we have the double integral wond too. And then zero two X minus one of one over X. Why? T x clerk. So let's take an anti derivative with respect to why so this one over X it's actually just a constant so really Teo Teo, one of ex What are beginning here. But we're just integrating. Why s so we'LL just get why evaluated X minus one So that's just X minus one the ex. Okay, and then we'LL distributes. So you have. Ah, one minus one of her ex the ex. So what is that x minus log? Perhaps a value of X but X is between one and two, so we don't need the absolute value Evaluated from one to two. Says there's going to be two units one minus. Wow. Goes to slog one. That's gonna be one minus log to remember the log of one zero