Question

Срочно вычислить определенный интеграл!

Answer 1

$intlimits^e_1 (x^{-1}+1)dx=ln|x|+x|^e_1=ln|e|+e-ln|1|-1=1+e-1=e$

$intlimits^0_{-1} frac{(3x-1)^4}{7}dx = frac{1}{21}intlimits^0_{-1}(3x-1)^4d(3x-1)=frac{1}{21}(frac{(3x-1)^5}{5}|^0_{-1})=\=frac{1}{21}(-frac{1}{5}+frac{1024}{5})=frac{1023}{21*5}=frac{341}{35}=9frac{26}{35}$

$intlimits^frac{pi}{12}_frac{pi}{6} (frac{2}{cos^22x}-cos2x) dx =- intlimits^frac{pi}{6}_frac{pi}{12} (frac{2}{cos^22x}-cos2x) dx=\=-(tg2x-frac{1}{2}sin2x|^frac{pi}{6}_frac{pi}{12})=-(sqrt3-frac{sqrt3}{4}-frac{sqrt3}{3}+frac{1}{4})=-(frac{5sqrt3+3}{12})$