Question

1) f(x) = 0; 3) f(x) = x-4; 2) f(x) = x10; 4) f(x) = sinx. = C​

Answer 1

Відповідь:

$1) f(x)=0\\ F(x)=\int\limits {0} \, dx =0+C.\\\\ 2) f(x)=x-4\\ F(x)=\int\limits {(x-4)} \, dx = \int\limits {x} \, dx - 4\int\limits {1} \, dx = \frac{x^2}{2}-4x=\frac{(x-8)x}{2}+C.\\\\ 3) f(x)=x^{10}\\\\ F(x)=\int\limits {x^{10}} \, dx = \frac{x^{11}}{11} +C.\\ x^{n} =\frac{x^{n+1}}{n+1} \\\\ 3) f(x)=sin(x)\\ F(x)=\int\limits {sin(x)} \, dx = -cos(x)+C.$