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Evaluate the given integral.$$\int\left(3 e^{x}-2 e^{y}+2 x-3 y+5\right) d x$$

$$3 e^{x}+x^{2}-2 x e^{y}-3 x y+5 x+c(y)$$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 6

Double Integrals

Partial Derivatives

Missouri State University

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

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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Evaluate the given integra…

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Evaluate the integral.…

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Evaluate the definite inte…

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03:08

Evaluate the integrals.

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03:15

Evaluate the integral.

Hello. My name is parking this for you. I'll show how to evaluate this integral. So here are expression here it's at the pockets and then we have the X. Which means with respect to X. So inside you see that we have some constant particular you know that 3223 and five are constants but we also have X. And Y. And this may be confusing. So how do you treat this? So remember the important part is your dx. So D X shows that we are integrating with respect to X. So everything inside here which is not an ex treated as a constant meaning these wise we're gonna treat them as constance. So answering this starting with the 1st 13 E. To the X. We know that we have our constant which is three. It was the integral of 84 X. You know that it remains to the eggs. Then we have minus so we have to get to the paul Y. And remember this whole expression in this world to each of Hawaii is a constant. So we just want to end and X. When we integrate so it's going to become too kinks E. To the polo Y. Queen freedom. We have to two X. And then if we integrate this you know that this becomes next to the port to And then with -3Y. Which is a constant as we would have three X. Y. three XY. Here. And then lastly we have plus five which becomes plus five X. Remember that the NDF plus C. Because this is an indefinite integral. Thank you for your time, Yeah.

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