The volume of the half box is $-\int_0^{\pi/4} \log\bigl(1 - \tfrac{1}{4\cos^2\theta}\bigr)\,d\theta$

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The volume of the half box is $-\int_0^{\pi/4} \log\bigl(1 - \tfrac{1}{4\cos^2\theta}\bigr)\,d\theta$ · Prove2Me