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improved further
on the other side.
on the other side.
We are not ready to find the volume. Note first that:
We are now ready to find the volume. Note first that:
:<math> dV = {\pi}r^2dx</math>
:<math> dV = {\pi}r^2dx</math>
:<math>V = \int_0^\frac{\pi}{4} {\pi}r^2\,dx</math>
:<math>V = \int_0^\frac{\pi}{4} {\pi}r^2\,dx</math>
The next insight is to express ''r'' in terms of ''x''. The variable ''r'' is the distance of the boundary from the axis about which it is rotated:
:<math>r = \sqrt 2 - \sec{x}}\,{\cos{x}}</math>
[[category:mathematics]]
[[category:mathematics]]
[[category:calculus]]
[[category:calculus]]