MathNet 1998 — Part 01 Question 79

Let $f(x) = 1 + \frac{x}{2} + \frac{x^{2}}{4} + \frac{x^{3}}{8} + \ldots$, for $-1 \leq x \leq 1$. Find $\sqrt{e^{\int_{0}^{1} f(x) d x}}$.