Все по действиям
ответ 84.
У²=х³ это полукубическая парабола, проходит через точки (0,0), (1,1), (-1,1).Её ветви в 1 и 4 четвертях .Так как даны ещё прямые х=0 и у=4, то область будет в 1 четверти.
Точки пересечения линий:
![y=4,y^2=x^3,\\\\16=x^3,x=\sqrt[3]{16}\\\\y^2=x^3\; \to \; y=\pm \sqrt{x^3}\\\\S=\int_0^{\sqrt[3]{16}}(4-\sqrt{x^3})dx=(4x-\frac{x^{\frac{5}{2}}}{\frac{5}{2}})|_0^{\sqrt[3]{16}}=4\cdot \sqrt[3]{16}-\frac{2}{5}(\sqrt[3]{16})^{\frac{5}{2}}=\\\\=4\cdot 2\sqrt[3]2-\frac{2}{5}\cdot (16)^{\frac{5}{6}}=8\sqrt[3]2-\frac{2}{5}\cdot 2^{\frac{10}{3}}=8\sqrt[3]2-\frac{2}{5}\cdot 8\sqrt[3]2=\frac{24}{5}\sqrt[3]2](https://tex.z-dn.net/?f=y%3D4%2Cy%5E2%3Dx%5E3%2C%5C%5C%5C%5C16%3Dx%5E3%2Cx%3D%5Csqrt%5B3%5D%7B16%7D%5C%5C%5C%5Cy%5E2%3Dx%5E3%5C%3B+%5Cto+%5C%3B+y%3D%5Cpm+%5Csqrt%7Bx%5E3%7D%5C%5C%5C%5CS%3D%5Cint_0%5E%7B%5Csqrt%5B3%5D%7B16%7D%7D%284-%5Csqrt%7Bx%5E3%7D%29dx%3D%284x-%5Cfrac%7Bx%5E%7B%5Cfrac%7B5%7D%7B2%7D%7D%7D%7B%5Cfrac%7B5%7D%7B2%7D%7D%29%7C_0%5E%7B%5Csqrt%5B3%5D%7B16%7D%7D%3D4%5Ccdot+%5Csqrt%5B3%5D%7B16%7D-%5Cfrac%7B2%7D%7B5%7D%28%5Csqrt%5B3%5D%7B16%7D%29%5E%7B%5Cfrac%7B5%7D%7B2%7D%7D%3D%5C%5C%5C%5C%3D4%5Ccdot+2%5Csqrt%5B3%5D2-%5Cfrac%7B2%7D%7B5%7D%5Ccdot+%2816%29%5E%7B%5Cfrac%7B5%7D%7B6%7D%7D%3D8%5Csqrt%5B3%5D2-%5Cfrac%7B2%7D%7B5%7D%5Ccdot+2%5E%7B%5Cfrac%7B10%7D%7B3%7D%7D%3D8%5Csqrt%5B3%5D2-%5Cfrac%7B2%7D%7B5%7D%5Ccdot+8%5Csqrt%5B3%5D2%3D%5Cfrac%7B24%7D%7B5%7D%5Csqrt%5B3%5D2)
1)хх+2ху+уу=25
хх+уу=21
2) ххх + 3ху(х+у)+ууу=125
ххх+ууу=125-30=95
1) 413-х/12+27=60
х/12=60-413-27
х/12=-380
х=-380*12
х=4560
2)41-216-3х/34=35
-3х/34=35-41+216
-3х/34=210
-3х=210*34
-3х=7140
х=7140:(-3)
х=-2380