Answer
$2.2532$
Work Step by Step
a) Given
$$y= \tan x,\ \ \ x=0,\ \ x=\pi/4,\ \ \ \text{about} \ \ x =\pi/2 $$
Since the volume of the generated solid given by
\begin{aligned}
V&=2\pi \int_a^b r(x)h(x)dx
\end{aligned}
Here
$$ r(x) = \frac{\pi}{2}- x,\ \ \ \ \ h(x) = \tan x $$
Then
\begin{aligned}
V&=2\pi \int_a^b r(x)h(x)dx\\
&= 2\pi \int_0^{\pi/4} \left(\frac{\pi}{2}-x\right)\tan xdx
\end{aligned}
b) Using calculator, we get
\begin{aligned}
V &= 2\pi \int_0^{\pi/4} \left(\frac{\pi}{2}-x\right)\tan xdx \\
&\approx 2.2532
\end{aligned}
