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Determine the region $R$ determined by the given double integral.$$\int_{-1}^{2} \int_{2}^{3} f(x, y) d x d y$$

$2 \leq x \leq 3$ and $-1 \leq y \leq 2$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 6

Double Integrals

Partial Derivatives

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Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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Determine the region $R$ d…

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Evaluate the double integr…

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For this problem, we are asked to determine the region are determined by the given double integral. So we can see we have in the interior the integral from 2-3 over X. And then the exterior integral Is the integral from negative 1 to 2 over why. So we can read off then that from that interior integral, whoops wait a little bit too far there. But whatever from that interior integral we have two is less than or equal to X is less than or equal to three. And then from the exterior integral We can read off that well, bottom boundary for why is negative one And upper boundary for why is positive three. So we have a rectangle with the dimensions specified.

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