Area approximation and (riemann?) sums

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Homework Help Overview

The discussion revolves around the approximation of the area of a region bounded by the curve y = 5/x and the line y = 0, as part of a calculus problem. The original poster, a first-year physics student, is exploring the use of rectangles to estimate this area.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the area using rectangles and has provided an initial estimate. They question whether the area bounded by y = 0 should be considered separately or if it is simply zero. Other participants clarify the nature of the problem and suggest that it is a single inquiry regarding the area between the two curves.

Discussion Status

The discussion is ongoing, with participants providing clarifications and insights. There is a recognition that the original estimate may not fully capture the nature of the area, as one participant mentions the area being infinite.

Contextual Notes

There is a potential misunderstanding regarding the interpretation of the problem, specifically whether the area bounded by y = 0 should be treated as a separate entity. The original poster's assumption about the area being zero is questioned.

science_rules
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Homework Statement


I am a first-year physics student learning calculus. my question is about the approximation of the area of a region bounded by y = 0.

Homework Equations


Use rectangles (four of them) to approximate the area of the region bounded by y = 5/x (already did this one), and y = 0. The height of the tallest rectangle is 5 units, on the y-axis. The numbers(width of the rectangles) on the x-axis are respectively: 1, 2, 3, 4 units.


The Attempt at a Solution


The first question was to find the area bounded by y = 5/x which i did: 5/1 + 5/2 +5/3 + 5/4 = approximately 10.4. I know this is correct.
Then the area bounded by y = 0 would just be zero i assume? is there a certain way to write this one or is it just zero? i cannot see what else it could be.
 
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I think they just mean to say find the area bounded BETWEEN the two curves y=5/x and y=0. It's just a single problem, which you already did. Not two separate problems.
 
ohhh. good to know. silly me. thankyou
 
science rules,
You might find it interesting that your estimate of 10.4 for the area bounded by the graph of y = 5/x and the x-axis (the line y = 0) is a very low estimate. In fact, the area of this region is infinite.
 

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