Find the volume of the solid obtained by rotating about the y-axis the | Mathematics I 2078

Mathematics I20785 marksNumerical: volume 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 the curves: - $y = x$ - $y = x^2$ - Axis of rotation: the y-axis Set the two curves equal: $x = x^2 \implies x^2 - x = 0 \implies x(x-1) = 0$ $\therefore x = 0 \quad \text{and} \quad x = 1$ On the interval $0 < x < 1$ , we have $x x^2$ , so $y = x$ is the upper curve and

Region bounded by the curves: - $y = x$ - $y = x^2$ - Axis of rotation: the y-axis Set the two curves equal: $$x = x^2 \implies x^2 - x = 0 \implies x(x-1) = 0$$ $$\therefore x = 0 \quad \text{and} \quad x = 1$$ On the interval $0 < x < 1$, we have $x x^2$, so $y = x$ is the upper curve and

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