Mixed Axis Revolution Volume

00:00 5 marks

Consider the region bounded by the curve \(y=x^2\), the x-axis, and the vertical lines \(x=0\) and \(x=2\). This region is divided into two parts by the vertical line \(x=1\). The left part (from \(x=0\) to \(x=1\)) is revolved about the x-axis using the disk method, and the right part (from \(x=1\) to \(x=2\)) is revolved about the y-axis using the shell method. Calculate the total volume of the solid obtained by combining the two revolved parts.

Hint Hint

Hint

Set up separate integrals for each section and remember to use the appropriate method for each axis of revolution.

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Complete Answer

\(\frac{77\pi}{10}\) cubic units.

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