Changing bounds of integration of a double integral

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Homework Help Overview

The discussion revolves around changing the bounds of integration for a double integral involving a region defined by a parabola and lines. Participants are exploring how to correctly set up the limits of integration based on the given problem context.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss their attempts to determine the correct bounds, with one original poster expressing uncertainty about the graphical representation of the region. Others provide feedback on the proposed limits and clarify the geometric interpretation of the area involved.

Discussion Status

The discussion has seen some progress, with one participant claiming to have figured out the correct bounds. However, there is still some debate regarding the interpretation of the region defined by the original limits of integration, indicating that multiple perspectives are being explored.

Contextual Notes

There is mention of a graphical representation that some participants find helpful for understanding the bounds, suggesting that visualizing the region is a key aspect of the problem. The original poster's initial approach did not yield the expected result, prompting further discussion.

yopy
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2rhtsom.jpg


Picture of the problem is listed above. I'm not sure how to switch the bounds of integration on it. Anyone here know how to go about this?

i tried doing it x^2 to 1 for y and then 0 to 1 for x but it didnt work out to be the write answer, the write answer after putting it in your calculator is about .40 ish

Normally when i do these kinds of problems i draw the bounds out, but I am not sure how these current bounds would even look.
 
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Hi yopy! :smile:

(try using the X2 tag just above the Reply box :wink:)
yopy said:
i tried doing it x^2 to 1 for y and then 0 to 1 for x but it didnt work out to be the write answer …

Well, that looks right to me …

it's just the area above the parabola y = x2

show us what you got.
 
i figured it out, the bounds turn into 0 to x^2 for respect to Y, and then 0 to 1 for respect to X

my problem was drawing the region they were integrating over. I got the right answer though, thanks.
 
tiny-tim said:
Hi yopy! :smile:

(try using the X2 tag just above the Reply box :wink:)


Well, that looks right to me …

it's just the area above the parabola y = x2


I don't think so. The limits of integration in the original problem indicate that the region is to the right of the parabola, not above it. The region is bounded by the parabola, the x-axis, and the line x = 1. Yopy's revised limits of integration describe this region.
 
oops!

Mark44 said:
I don't think so. The limits of integration in the original problem indicate that the region is to the right of the parabola, not above it. The region is bounded by the parabola, the x-axis, and the line x = 1. Yopy's revised limits of integration describe this region.

oops! :redface: i should have drawn it! :rolleyes:

thanks Mark! :smile:
 

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