Finding the Antiderivative of 2xy

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Homework Help Overview

The problem involves finding the antiderivative of the expression 2xy, with the context focusing on the variables involved in the integration process.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to clarify which variable to integrate with respect to, considering both x and y are variables. There is an attempt to express the antiderivative, but uncertainty about the correct approach is evident.

Discussion Status

The discussion is active, with participants questioning the assumptions regarding the variables and providing different expressions for the antiderivative based on the chosen variable of integration. No consensus has been reached on the preferred method.

Contextual Notes

Participants are navigating the ambiguity of integrating with respect to either x or y, which affects the resulting expressions for the antiderivative.

BJducky
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Homework Statement


It is simple: find the antiderivative of 2xy.


Homework Equations





The Attempt at a Solution


I am inclined to say that it equals (xy)^2 +c, but can't help but feel i have left out something.
 
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What are you integrating with respect to? Are both x and y variables?
 
Yes, they are both variables.
 
rock.freak667 said:
What are you integrating with respect to? Are both x and y variables?

BJducky said:
Yes, they are both variables.
Then answer the question! You want to find the anti-derivative with respect to which variable?

[tex]\int 2xy dx= x^2y+ C[/tex]

[tex]\int 2xy dy= xy^2+ C[/tex]

Choose one!
 

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