Problem

Use the region $R$ with the indicated boundaries …

08:52

Problem 50 Medium Difficulty

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

$=[1-\ln 2]$

Topics

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Book Cover for Calculus with Appli…

Calculus with Applications

Chapter 9

Multivariable Calculus

Section 6

Double Integrals

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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

Matt J.

Georgia Southern University

Topics

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Book Cover for Calculus with Appli…

Calculus with Applications

Chapter 9

Multivariable Calculus

Section 6

Double Integrals

Top Calculus 3 Educators

Lily A.

Johns Hopkins University

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Caleb E.

Baylor University