- #1

igorrn

- 2

- 0

- Homework Statement
- Give the area marked in the graph (graph as jpg file)

- Relevant Equations
- x = cos y

y = cos x

x E [0,1] and y E [0,1]

I tried this:

X = cos(y) → y = arccos(x) for x E(-1,1) and y E (0,2)

Then:

There's a point I(Xi,Yi) in which:

Cos(Xi) =Arccos(Xi)

Then I said area1 (file: A1)

A1 = ∫cosx dx definite in 0, Xi

And A2 (file:A2):

A2 = ∫cosy dy definite in 0, Yi

And the overlapping area as A3 (file: A3):

A3 = ∫Yi dx definite in 0, Xi

And total area, then, is:

A = A1 + A2 - A3

I had trouble finding the value of Xi though. The best Approach I could find is 3/4, but I had not found a method further narrow the aprroach answer. I think Xi is an irrational number, I'd want to know if it has a name and definition to it like Pi or Euler's Number to find it.

I'd want to know if there's another method to calculating this area also.

X = cos(y) → y = arccos(x) for x E(-1,1) and y E (0,2)

Then:

There's a point I(Xi,Yi) in which:

Cos(Xi) =Arccos(Xi)

Then I said area1 (file: A1)

A1 = ∫cosx dx definite in 0, Xi

And A2 (file:A2):

A2 = ∫cosy dy definite in 0, Yi

And the overlapping area as A3 (file: A3):

A3 = ∫Yi dx definite in 0, Xi

And total area, then, is:

A = A1 + A2 - A3

I had trouble finding the value of Xi though. The best Approach I could find is 3/4, but I had not found a method further narrow the aprroach answer. I think Xi is an irrational number, I'd want to know if it has a name and definition to it like Pi or Euler's Number to find it.

I'd want to know if there's another method to calculating this area also.