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improved
:<math>V = \int_0^\frac{\pi}{4} {\pi}(2 - 2\sqrt2\sec{x}\,\tan{x} + (\sec{x}\,\tan{x})^2\,dx</math>
:<math>V = \int_0^\frac{\pi}{4} {\pi}(2 - 2\sqrt2\sec{x}\,\tan{x} + (\sec{x}\,\tan{x})^2\,dx</math>
The only challenging part of this [[integral]] is the last term, which must be [[integrated by parts]]:
:<math>\int_0^\frac{\pi}{4}(\sec{x}\,\tan{x})^2\,dx</math>
[[category:mathematics]]
[[category:mathematics]]
[[category:calculus]]
[[category:calculus]]