Question

Определённые интегралы, 3 задачи очень

Answer 1

$\displaystyle\\1)S=-\int\limits^3_{-3} {x^2-9} \, dx=\int\limits^3_{-3} {9-x^2} \, dx=(9x-\frac{x^3}{3})\mid^3_{-3}=9*3-\frac{3^3}{3}-\\\\\\ -\bigg(9*(-3)+\frac{3^3}{3}\bigg)=27-9-(-27+9)=18-(-18)=36\\\\\\2)V=\pi\int\limits^3_2 {\frac{1}{x^2} } \, dx=\pi(-\frac{1}{x})\mid^3_2=\pi\bigg(-\frac{1}{3}-(-\frac{1}{2})\bigg) =\frac{\pi}{6}\\\\\\ 3)S=\int \upsilon(t)dt\\\\\int\limits^5_0 {t^2-t+3} \, dt =\bigg(\frac{t^3}{3}-\frac{t^2}{2}+3t)\bigg)\mid^5_0=\frac{5^3}{3}-\frac{5^2}{2}+3*5-\\\\\\$

$\displaystyle\\-\bigg(\frac{0}{3}-\frac{0}{2}+3*0\bigg)=\frac{125}{3}-\frac{25}{2}+15=\frac{265}{6}$