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Determine the region $R$ determined by the given double integral.$$\int_{0}^{1} \int_{y^{2}}^{\sqrt{y}} f(x, y) d x d y$$

Same as 23

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 6

Double Integrals

Partial Derivatives

Johns Hopkins University

Missouri State University

Harvey Mudd College

University of Nottingham

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 from 0 to 1 of the integral from Y squared up to root Y of F. Of X. Y Dx Dy. So we can read off from the interior integral that we have X is going to be greater than or equal to y squared and less than or equal to the square root of Why? Then we have that. Why must be between zero and 1? So we would have that the region determined by the double integral is the interior of this region here. But we can alternatively note that we have that the lower bound for X is at X equals Y squared, which corresponds to Y equals the square root of X. And at the upper bound we have X equals root. Why? Which corresponds to Why equals X squared. So we can see that this is actually the same region as what we saw in the previous problem.

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