Question

помогите пожалуйста
2 а)​

Answer 1

Ответ:

$1)\ \ F(x)=\int \dfrac{2\, dx}{\sqrt{1-x}}=2\cdot \dfrac{-1}{2\sqrt{1-x}}+C=-\dfrac{1}{\sqrt{1-x}}+C\\\\\\A(-3;1)\ \ \to \ \ F(-3)=1\ \ \to \ \ 1=-\dfrac{1}{\sqrt{1+3}}+C\ \ ,\ \ 1=-\dfrac{1}{2}+C\ ,\\\\C=\dfrac{3}{2}\\\\F(x)\Big|_{A(-3;1)}=-\dfrac{1}{\sqrt{1-x}}+\dfrac{3}{2}$

$2)\ \ F(x)=\int \Big(3+\dfrac{1}{\sqrt{5-x}}\Big)\, dx=3x+\dfrac{-1}{2\sqrt{5-x}}+C=3x-\dfrac{1}{2\sqrt{5-x}}+C\ ,\\\\\\A(-4;0)\ \ \to \ \ F(-4)=0\ \ \to \ \ 0=-12-\dfrac{1}{2\sqrt{5+4}}+C=12-\dfrac{1}{2\cdot 3}=\dfrac{71}{6}+C\ ,\\\\C=-\dfrac{71}{6}\\\\F(x)\Big|_{A(-4;0)}=3x-\dfrac{1}{2\sqrt{5-x}}-\dfrac{71}{6}$