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Evaluate the double integral $\iint_{0}^{2} \int_{x}^{2} e^{y^{2}} d y d x$.

$$\frac{e^{4}-1}{2}$$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 6

Double Integrals

Partial Derivatives

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Lectures

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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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02:56

Evaluate the double integr…

01:01

Evaluate the given double …

01:48

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01:47

in discussion. We live in a double Integral went out integral from the 21 on D. Why? But in I have the bomb Y Juneja y yes. And then we have no one plus two X square plus two y square de y the X. Yeah, and let's try to do the in the first on the side here. So we have in the girl from why to the to y one plus two x square last July square t x notice that X will be the variable. So why will be the constant? And then we get untidy lifting the one equal to the X plus untidy derivative Amazon echo to that to export 3/3 Anti derivative isn't encouraging that you y square X If I looted from why to the two why and now everyone, this Joe here into the x Not why Then we get equal to the two y plus nah is only half the items jewelry 16. Why about three other three and then plus this one will be the Judum Still be far. Why about three subjecting a woman? Why inside we have the Y plus two y about three hour three plus that to wipe out three. And now it will simplify this one. Get echoed. You find about three. We have 123 and four here. So we have, uh, 16 of a three and then blood far minus that. Two out of three minus do. So we get me go to the 20 out of 31 about three. Find out why we have to one minus wise. We're gonna plus. Why here? So this will be the answer for the in the girl we're looking to hear. So we had in coaching the integral from 0 to 1. 23. Why about three plus why de y And now I'm time derivative. This one equal to the five y. About 4/3 last. Why this one? Gonna white square over to evaluated from the 21 Then we get equal June 15 out of three plus a half minus zero. Then this one. Get Geico. Jew? Yeah, we have the 10 plus three will be 13/6. And that's gonna be the answer. Yeah,

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