Chapter 6: Applications of Definite Integrals - Section 6.1 - Volumes Using Cross-Sections - Exercises 6.1 - Page 324: 60

$1$

Integrate the integral to calculate the volume as follows: We have: $V= \pi \times \int_{a}^{b} f^2(x) dx =6 \pi$ or, $ \int_{a}^{b} (f(x)+2)^2- 4 dx=10 \pi$ or, $ \int_{a}^{b} (f(x)+2)^2-4 dx=10$ or, $6+ (4) \int_{a}^{b} f(x) dx=10$ Thus, our answer is: $\int_{a}^{b} f(x) dx= 1$