Chapter 4 - Integrals - 4.3 The Fundamental Theorem of Calculus - 4.3 Exercises - Page 328: 44

$$\frac{215}{648}$$

Given $$y=x^{-4}, \ \ 1 \leqslant x \leqslant 6$$ From the graph of the region, we can observe that area of the bounded region approximately equal to $\frac{1}{10}$ area of the rectangle with width 1 and length 5 $$\text{Area} \approx \frac{1}{10} (1)(5)=0.5 $$ Now we use integration \begin{aligned} \text{Area}&= \int_1^{6}{x}^{-4}dx\\ &= \frac{-1}{3}x^{-3}\bigg|_{1}^{6} \\ &= \frac{-1}{3}[\frac{1}{6^3}-1]\\ &= \frac{215}{648} \end{aligned}