Question

Найти значение выражения:
$80( sqrt{3} +1) intlimits^ frac{ pi }{10} _ frac{ pi }{20} {sin(10x+ frac{ pi }{3} )} , dx$

Answer 1

$80(sqrt{3}+1) intlimits^frac{pi}{10}_{frac{pi}{20}} sin(10x+frac{pi}{3})dx=\\ 80(sqrt{3}+1)*-frac{1}{10}cos(10x+frac{pi}{3})|^{frac{pi}{10}}_{frac{pi}{20}}=\\ 80(sqrt{3}+1) * -frac{1}{10}*(cos(pi+frac{pi}{3})-cos(frac{pi}{2}+frac{pi}{3}))=\\ -8(sqrt{3}+1)(cosfrac{4pi}{3}-cosfrac{5pi}{6})=-8(sqrt{3}+1)(frac{1-sqrt{3}}{2})=8$