# Just a Cal 2 Problem

Calculus Level 3

Let $$f:\mathbb{R} \to \mathbb{R}$$ be a function with derivative of any order. Suppose $$f$$ has the property that $$f(x)+f(-x)=1$$ $$\forall x\in \mathbb{R}$$

Find the value of $\int_{-1}^1 x^2f(x)\, dx$

Bonus: Under the property $$f(x)+f(-x)=k$$ $$\forall x\in \mathbb{R}$$ and some non-zero constant $$k$$, find $\int_{-a}^a x^{2n}f(x)\, dx$ where $$n\in \mathbb{Z}^+$$ and $$a\in \mathbb{R}^+$$

×