Find the volume of the solid obtained by rotating about the y-axis the | Mathematics I 2077

Mathematics I20775 marksNumerical: Volume of solid of revolutionVolumes of cylindrical cells

Find the volume of the solid obtained by rotating about the y-axis the region between $y = x$ and $y = x^2$ . [5]

Find the volume of the solid obtained by rotating about the y-axis the region between $y = x$ and $y = x^2$. [5]

Region bounded by curves: $y = x$ and $y = x^2$ - Axis of rotation: the $y$ -axis All data present. Set the curves equal: $x = x^2 \implies x^2 - x = 0 \implies x(x-1) = 0$ $x = 0 \quad \text{and} \quad x = 1$ At $x = 0.5$ : $y = x = 0.5$ and $y = x^2 = 0.25$ . So $y = x$ is above $y = x^2$ on...

Region bounded by curves: $y = x$ and $y = x^2$ - Axis of rotation: the $y$-axis All data present. Set the curves equal: $$x = x^2 \implies x^2 - x = 0 \implies x(x-1) = 0$$ $$x = 0 \quad \text{and} \quad x = 1$$ At $x = 0.5$: $y = x = 0.5$ and $y = x^2 = 0.25$. So $y = x$ is above $y = x^2$ on...

Find the volume of the solid obtained by rotating about the y-axis the region between y = x and y = x2.