Question

Срочно будьласка розв'яжіть

Answer 1

Ответ: S=343/3 кв. ед.

Объяснение:

$y=x^2-3x-14\ \ \ \ \ \ y=3x+6-x^2\ \ \ \ \ \ S=?\\\\x^2-3x-14=3x+6-x^2\\\\2x^2-6x-20=0\ |:2\\\\x^2-3x-10=0\\\\x^2-5x+2x-10=0\\\\x(x-5)+2(x-5)=0\\\\(x-5)(x+2)=0\\\\x_1=5\ \ \ \ x_2=-2.$

$\displaystyle\\S=\int\limits^5_{-2} (3x+6-x^2-(x^2-3x-14)) \, dx= \int\limits^5_{-2} (3x+6-x^2-x^2+3x+14)) \, dx= \\\\\\=\int\limits^5_{-2} (-2x^2+6x+20) \, dx =dx =\int\limits^5_{-2} 2(-x^2+3x+10) \, dx =-2\int\limits^5_{-2} (x^2-3x-10) \, dx =\\\\=-2(\frac{x^3}{3}-\frac{3x^2}{2}-10x)\ |_{-2}^5 =\\\\=-2(\frac{5^3}{3} -\frac{3*5^2}{2}-10*5-(\frac{(-2)^3}{3}-\frac{3*(-2)^2}{2} -10*(-2))=\\\\\\=-2(\frac{125}{3}-\frac{75}{2} -50+\frac{8}{3} +\frac{12}{2} -20)=-2(\frac{133}{3}-\frac{63}{2}-70)=$

$\displaystyle\\=\frac{133*(-2)}{3} +63+140=-\frac{266}{3}+203 =\frac{-266+203*3}{3}=\frac{609-266}{3} =\frac{343}{3}.$