Lời giải

\(\textbf{a)}  \)
\( V = \pi \int_{0}^{\frac{\pi}{4}} (\tan^2 x) \, dx = \pi (\tan x - x ) \bigg|_{0}^{\frac{\pi}{4}} \)

\( V = \pi \left(1 - \frac{\pi}{4}\right) = \pi - \frac{\pi^2}{4} \)

\(\textbf{b)}  \)
\( 1 - x^2 = 0 \iff x = \pm 1 \)  

\( V = \pi \int_{-1}^{1} (1 - x^2)^2 \, dx = \pi \int_{-1}^{1} \left(1 - 2x^2 + x^4\right) \, dx \)

     \( = \pi (x - \frac{2x^3}{3} + \frac{x^5}{5}) \bigg|_{-1}^{1} \)

     \(  = \frac{16\pi}{15} \)