Answer
We need to use the shell model as follows:
$V=\int_p^{q} (2 \pi) \cdot (\space radius \space of \space shell) ( height \space of \space Shell) \space dx$
$ \implies V= \int_0^{1} (2 \pi) \cdot (x)[2-x-x^2] dx$
Now, $V=2 \pi [x^2-\dfrac{x^3}{3}-\dfrac{x^4}{4}]_0^1$
or, $= 2 \pi \times (1-\dfrac{1}{3}-\dfrac{1}{4})$
or, $=\dfrac{5 \pi}{6}$
Work Step by Step
We need to use the shell model as follows:
$V=\int_p^{q} (2 \pi) \cdot (\space radius \space of \space shell) ( height \space of \space Shell) \space dx$
$ \implies V= \int_0^{2} (2 \pi) \cdot (x)[2-x-x^2] dx$
Now, $V=2 \pi [x^2-\dfrac{x^3}{3}-\dfrac{x^4}{4}]_0^1$
or, $= 2 \pi \times (1-\dfrac{1}{3}-\dfrac{1}{4})$
or, $=\dfrac{5 \pi}{6}$
