Find the volume of the solid obtained by rotating about the y-axis the | Basic Mathematics 2081

Basic Mathematics20815 marksNumerical: volume of solidVolume of solids of revolution

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

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

Curve 1: $y = x$ - Curve 2: $y = x^2$ - Axis of rotation: the y-axis - Region: bounded between the two curves All data needed is present. Step 1: Intersection points $x = x^2 \implies x^2 - x = 0 \implies x(x-1) = 0$ So $x = 0$ or $x = 1$ , giving intersection points $(0,0)$ and $(1,1)$ . Step ...

Curve 1: $y = x$ - Curve 2: $y = x^2$ - Axis of rotation: the y-axis - Region: bounded between the two curves All data needed is present. Step 1: Intersection points $$x = x^2 \implies x^2 - x = 0 \implies x(x-1) = 0$$ So $x = 0$ or $x = 1$, giving intersection points $(0,0)$ and $(1,1)$. Step ...

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