Integration Applications Question

[Shakattack12]

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.

 

[scottdave]

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?

 

[Shakattack12]

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.

 

[scottdave]

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?

 

[Shakattack12]

Yeah the arcs were symmetrical. Thanks for the help I figured it out.