Question

найти первообразную для функции f(x)= sin(2x + p/3) + cos(3x + p/4) если F(p/12)=1

Answer 1

$F(x)=-frac{cos(2x+frac{pi}{3})}{2}+frac{sin(3x+frac{pi}{4})}{3}+C\F(frac{pi}{12})=-frac{cos(2timesfrac{pi}{12}+frac{pi}{3})}{2}+frac{sin(3timesfrac{pi}{12}+frac{pi}{4})}{3}+C=\-frac{cos(frac{pi}{2})}{2}+frac{sin(frac{pi}{2})}{3}+C=frac{1}{3}+C=1\\C=frac{2}{3}\\F(x)=-frac{cos(2x+frac{pi}{3})}{2}+frac{sin(3x+frac{pi}{4})}{3}+frac{2}{3}$