**Toolbox:**

- Area bounded by the curve $t=f(x),$ the x-axis and the ordinates $x=a,x=b$ is $\int \limits_a^b f(x) dx $ or $ \int \limits _a^b y dx $
- If the curve lies below the x-axis for $a \leq x \leq b,$ then the area is $\int \limits_a^b (-y) dx=\int \limits_a^b (-f(x))dx$

Step 1:

Volume of solid generated by resolving the area between $y=x^3 ,y=0,y=1$ about y-axis

$V= \pi \int \limits_0^1 x^2 dy$

$\quad= \pi \int \limits_0^1 y^{\large\frac{2}{3}} dy$

$\quad=\large\frac{3}{5} $$ \pi \bigg[y^{\large\frac{5}{3}} \bigg]_0^1$

$\quad=\large\frac{3 \pi}{5}$