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Determine the region $R$ determined by the given double integral.$$\int_{-1}^{3} \int_{2}^{4} f(x, y) d y d x$$

(a) $-1 \leq x \leq 3,$ and $2 \leq y \leq 4$ Note: Mistake in the diagram at the end (y was from 2 to 5, it should be from 2 to 4)

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 double integral of Well, let's see here, we have the integral from negative one. Up to three of the integral from 2 to 4 of F of x y Dy Dx where F is not specified. So if we read off this first, this interior integral, We can see that we have, why is going to be between two and 4. Then looking at the exterior integral, you can write it as negative one or negative 123 of capital F of X Y DX. So we can see that this is going to be for x between negative one and positive three. So we can tell then that we have a rectangle From -1 to positive three And from it's from 2 to 4. So, let's see here. So this is the region that we're integrating over.

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