 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2014/5/solution

x

is a disk of radius

r = x^{2}

, so its area is

π x^{4}

. Slicing along the axis gives

V = \int_{0}^{1} π x^{4} d x = \frac{π}{5} .

The result uses the coordinate units implicit in the source's relation between radius and axial coordinate.

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