Question Type 4: Finding the volume of revolution of a region about the x-axis Exercises

Calculate the volume of the solid generated by revolving the region under the curve $y=2x - x^2$ from $x=0$ to $x=2$ about the $x$-axis.

Calculate the volume of the solid formed by revolving the region under $y=2x - x^2$ for $0\le x\le1$ about the $y$-axis using the shell method.

Determine the volume of the solid obtained by revolving the region under $y=2x - x^2$ from $x=1$ to $x=2$ about the $x$-axis.

Compute the volume of the solid formed by revolving the region under $y=2x - x^2$ from $x=0$ to $x=2$ about the line $y=2$.

Find the volume of the solid generated by revolving the region under $y=2x - x^2$ from $x=0$ to $x=2$ about the line $x=-1$.

Find the volume of the solid formed when the region under $y=2x - x^2$ between $x=0$ and $x=2$ is revolved about the $y$-axis.

Compute the volume of the solid generated by revolving the region under $y=2x - x^2$ from $x=0$ to $x=2$ about the line $y=-1$.

Find the volume of the solid generated by revolving the region bounded by $y=2x - x^2$ and $y=x$ for $0\le x\le1$ about the $x$-axis.

Find the volume of the solid generated by revolving the region under $y=2x - x^2$ from $x=0$ to $x=2$ about the vertical line $x=3$.

Calculate the volume of the solid obtained by revolving the region bounded by $y=2x - x^2$ and $y=x$ for $0\le x\le1$ about the $y$-axis.

Determine the volume of the solid generated by revolving the region between $y=2x - x^2$ and $y=x$ for $0\le x\le1$ about the line $y=1$.

Determine the volume of the solid generated by revolving the region under $y=2x - x^2$ from $x=0$ to $x=2$ about the $y$-axis using the disk method by inverting $x$ as a function of $y$.