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Determine the region $R$ determined by the given double integral.$$\int_{0}^{8} \int_{0}^{\sqrt{y}} f(x, y) d x d y$$

Same as 27

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 determined or the region are determined by the given double double integral. So, to begin we can see that for the interior integral we have X. Or we are integrating over X from zero to route why? So we have zero is less than or equal to X is less than or equal to root. Why. And we have from the exterior integral. We're integrating over Why and it's between zero and eight. So we can read off essentially that we are bounded by the lines, X equals zero, X equals root. Why? Which we can translate into why equals X squared. And let's see here. We would additionally have Well, yeah, the only other bound would be Y equals eight. So if we were to plot out of the region one second here, we'll find that the region is actually identical to the region for the previous problem.

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