How Do You Calculate the Mass of a Triangle with Variable Density?

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Homework Help Overview

The problem involves calculating the mass of a triangle defined by the x and y axes and the line x + 2y = 4, with a variable density function f(x,y) = 2y. Participants are exploring how to set up the integration for this calculation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to convert the line equation for y and consider the limits of integration for the double integral. There are questions about the integration method to use, such as integration by parts or substitution.

Discussion Status

The discussion is ongoing, with some participants offering guidance on setting up the integral and others questioning the limits of integration and the correctness of the results obtained. There is no explicit consensus on the final answer, and further clarification is sought regarding the calculations.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can share or the methods they can use. There is also a noted discrepancy in the interpretation of the limits of integration.

mp252
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hi i am having great difficulties doing this i was wondering if anyone could start me of thanks,
a triangle is formed by the x, y - axes and the line x+2y=4. the density is given by f(x,y)= 2y. I know that i need to convert the line for y but from there on i have no idea, much abliged
 
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take the double integer of 2y where y ranges from 0 to (x+4)/2 and x ranges from 0 to 4
 
thanks for that i have now got to the part of 10x/2 dx I am not to sure how to integrate this, should i do it in parts or substitution?
 
i think i got it now the answer is 40kg? is this correct
 
mp252 said:
i think i got it now the answer is 40kg? is this correct

No, the area of the triangle is 4 and the maximum density is 4. That can't possibly be right. You'd better show us what you did. BTW why was MiniST wrong in saying the limit of integration is (4+x)/2?
 

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