Question

Для функции f(x)=3 sinx+4/x в квыдрате.найти первообразную,если f(п/2)=0

Answer 1

$f(x) = 3sinx + (\frac{4}{x})^{2}\\ F(x) = -3cosx + 16*\frac{x^{-1}}{-1} = - 3cosx - \frac{16}{x} + C\\ F(\frac{\pi}{2}) = 0\\ - 3cos\frac{\pi}{2} - 16*\frac{2}{\pi} + C= 0\\ C = 3cos\frac{\pi}{2} + \frac{32}{\pi} \\ C = 0 + \frac{32}{\pi} \\ C = \frac{32}{\pi} \\ F(x) = - 3cosx - \frac{16}{x} + \frac{32}{\pi}$