Question

алгебра 5.13(1,2)помогите кто знает ​

Answer 1

Ответ:

$1)\ \ \displaystyle y=x^2\ ,\ y=3-2x\\\\S=\int\limits^1_{-3}\ (3-2x-x^2)\, dx=\Big(3x-x^2-\frac{x^3}{3}\Big)\Big|_{-3}^1=3-1-\frac{1}{3}-\Big(-9-9+9\Big)=\\\\\\=2-\frac{1}{3}+9=10\frac{2}{3}$

$2)\ \ y=x^2\ ,\ y=2x-x^2\\\\x^2=2x-x^2\ \ ,\ \ 2x^2-2x=0\ \ ,\ \ 2x(x-1)=0\ \ ,\ \ x_1=0\ ,\ x_2=1\\\\\displaystyle S=\int\limits^1_0\, (2x-x^2-x^2)\, dx=\int\limits^1_0\, (2x-2x^2)\, dx=\Big (x^2-\frac{2x^3}{3}\Big)\Big|_0^1=\\\\\\=1-\frac{2}{3}=\frac{1}{3}$