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Determine the region $R$ determined by the given double integral.$$\int_{0}^{2} \int_{0}^{x} f(x, y) d y d x+\int_{2}^{4} \int_{0}^{4-x} f(x, y) d y d x$$

Same as 25

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 6

Double Integrals

Partial Derivatives

Oregon State University

Harvey Mudd College

Baylor University

Idaho State University

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. Where we have the some of the integral from 0 to 2 of the integral from zero to X of F of X. Y Dy dx plus. The integral from 2 to 4 of the integral from 0 to 4 minus X. Of F F. Excuse me? Of F of X Y Dy dx. So to begin we can see that what we'll have to do is split this apart into two different regions. For our first term we have that we're integrating why from zero to X. So we have why is greater than zero? Less than X. And for the external integral we have that X is between zero and 2. Then for the second term we have, why is between zero and 4 -1. And we have that X is between two and four. So we can see that this is essentially a piecewise function. If we were to plot this out, what we'll see is that now I'm actually reusing the plot from the previous problem, we have that this is term one to the left and this is term too to the right. So we can see that the region that we are integrating over is actually the same as the region for the previous problem

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