Not that Snake!

Calculus Level 5

Let \(f(x) \) be a function satisfying \(f(x)= x-x^2\) where \(0\leq x \leq 1 \), and \(f(x+1) = f(x) \) for \(x\in \mathbb R\).

If \(\displaystyle g(x)= \int_0^x f(t) \, dt \), find \(g(6.3) \).

Give your answer upto 3 decimal places.

Notation: \(\mathbb R \) denotes the set of real numbers.

Bonus: Find the general expression for \(g(x) \).

See its sister problem: Not that Snake again!


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