Integration Applications Question

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Homework Help Overview

The discussion revolves around finding the area of a shaded region within a square, described as "the pink," without a specific equation for its boundary. The problem is situated in the context of integration applications, with the area of the square given as 1 square unit.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the possibility of the shaded area being a section of a circle and question the original poster's reasoning for arriving at the area of (π/2) - 1. There is discussion about the implications of the area being derived from a lens shape formula and the need for integration methods.

Discussion Status

The conversation has led to some productive questioning regarding the geometry of the problem, including the symmetry of the arcs and the relationship between the quarter circle and the square. While the original poster expresses gratitude for the help, it remains unclear if a definitive conclusion has been reached.

Contextual Notes

The original poster notes a lack of information regarding the boundary line of the shaded area and the potential constraints of using established area formulas in the context of integration applications.

Shakattack12
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Homework Statement


Hi, the question just states find the area of the pink, within a square, without giving an equation for the pink boundary line. I did look up the formula for the lens shape but was wondering how to do this with integration. The area of the square is 1 un2.

Sorry about the image, wasn't sure if I could post a textbook question.

Homework Equations

The Attempt at a Solution


Using the area of a lens shape I got (π/2) - 1.
 

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Hmm. Any more info? Is it a section of a circle with a radius 1 unit, for example? What did you do to come up with your answer of (pi/2) - 1? So if it is a quarter circle, for example, what can you say about the area outside of the shaded area?
 
That's all the information was. The diagonal of the square is √2 using Pythagoras but nothing else I could extrapolate. I got (π/2) -1 by finding a rule for the area of a lens and went from there. The textbook says the answer is (π/2) - 1 but it's in integral applications so I probably can't just use a rule for area.
 
Suppose that one of the arcs is a quarter circle. What is the radius of that circle? From that, what is the area of that quarter circle (not your shaded area, but from the center of the circle to the edge. Subtract that from the area of the square. Do you see any symmetry?
 
Yeah the arcs were symmetrical. Thanks for the help I figured it out.
 

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