Chapter 5 - Section 5.4 - The Fundamental Theorem of Calculus - Exercises - Page 320: 34

$[\frac{1}{\pi\cdot ln\pi}]\cdot(1-\frac{1}{\pi})\approx0.1896$

$\int_{-1}^{0} ({\pi^{x-1}})dx=[\frac{\pi^{x-1}}{ln\pi}]_{-1}^{0}=[\frac{\pi^{0-1}}{ln\pi}]-[\frac{\pi^{-1-1}}{ln\pi}]=[\frac{1}{\pi\cdot ln\pi}]-[\frac{1}{\pi^2\cdot ln\pi}]=[\frac{1}{\pi\cdot ln\pi}]\cdot(1-\frac{1}{\pi})\approx0.1896$