Modulus + Integral

Calculus Level 3

\[\ Let \ S = \int^{+\sqrt{2}}_{-\sqrt{2}} (1- |1-x^2|) dx \] S can be written in the form \(\frac{a \sqrt{2} +b}{c}\), where a,b, c are integers and the fraction is in its simplest form. What is the value of a+b+c?

Assumption and details:

1) |x| represents the modulus (distance from 0) of x

2) An example of a fraction in its simplest form: \(\frac{17 \sqrt{2} +10}{9}\) as 17 and 9 are coprime as well as 10 and 9.


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