Так как это куб, то диагонали каждой грани - диагонали квадрата, угол = 90
Согласно таблице интегралов
![\int_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}}\frac{dx}{\sqrt{1-x^2}}=\arcsin x|_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}}=](https://tex.z-dn.net/?f=%5Cint_%7B%5Cfrac%7B1%7D%7B2%7D%7D%5E%7B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%7D%5Cfrac%7Bdx%7D%7B%5Csqrt%7B1-x%5E2%7D%7D%3D%5Carcsin+x%7C_%7B%5Cfrac%7B1%7D%7B2%7D%7D%5E%7B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%7D%3D)
![=\arcsin \frac{\sqrt{3}}{2}-\arcsin \frac{1}{2}=\frac{\pi}{3}-\frac{\pi}{6}=\frac{\pi}{6}](https://tex.z-dn.net/?f=%3D%5Carcsin+%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D-%5Carcsin+%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B%5Cpi%7D%7B3%7D-%5Cfrac%7B%5Cpi%7D%7B6%7D%3D%5Cfrac%7B%5Cpi%7D%7B6%7D)
Ответ:
![\frac{\pi}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%7D%7B6%7D)
<span>1)
2x</span>²<span>+ 24xy +72y</span>² = 2 ·(х²+12ху+36у²) = 2·(х+6у)² = 2·(х+6у)(х+6у)
<span>2)
-8a</span>⁵<span> +8а</span>³<span> - 2а = -2а</span>·(4а⁴-4a²+1) = -2a·(2a²-1)² = -2a·(2a²-1)(2a²-1)
<span>3)
5a</span>³<span> - 40b</span>⁶ = 5a³ ·(1-8b³) = 5a³ ·(1³ - (2b)³) = 5a³·(1-2b)(1+2b+4b²)
<span>4)
8а</span>³<span> -аb - a</span>²<span>b + а</span>² = a·(8a²-b-ab+a)
Решение смотри в приложении