Mathematics I20755 marksNumerical: Volume of solid of revolutionVolumes of cylindrical cells
Find the volume of the resulting solid which is enclosed by the curve y = x and y = x2, is rotated about the x-axis.
Find the volume of the resulting solid which is enclosed by the curve $y = x$ and $y = x^2$, is rotated about the x-axis. [5]
- Curves: $y = x$ and $y = x^2$ - Axis of rotation: the x-axis $$x = x^2 \implies x^2 - x = 0 \implies x(x-1) = 0$$ $$\therefore x = 0, \quad x = 1$$ On $[0,1]$, since $x \geq x^2$, the line $y = x$ is the upper (outer) curve and $y = x^2$ is the lower (inner) curve. Rotating about the x-axis: $$...