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Determine the region $R$ determined by the given double integral.$$\int_{0}^{6} \int_{x^{2}}^{6 x} f(x, y) d y d x$$

Bounded by $y=6 x$ and $y=x^{2}$ see Fig. Ex. 12.

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 from zero or from the In the interior we have from X squared up to six X over Y. And then in the exterior we have from 0 to 6 over X. So we can tell then that the lower boundary on why is X squared the upper boundary on why is six X. And then we have that X is bounded below by zero and bounded above by six. Now it's not specified that you have to do this for the problem. But taking a look at a plot, You can see that we have, this is our region are where above. We have y equals six X. Below. We have Y equals X squared. And we can see that we're going from X equals zero up to X equals six.

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