Question

Интегралы
Помогите прошу

Answer 1

$displaystyle 1) int^2_{-1}dx=0$
$displaystyle 5) int^4_1 (3-2x)dx=3x-x^2 big|^4_1=12-16-(3-1)=-4-2=-6$
$displaystyle 32) int^1_{-1} x^2dx= frac{x^3}{3} big|^1_{-1}= frac{1}{3}-(- frac{1}{3})= frac{2}{3}$
$displaystyle 18) int ^{ frac{pi}{2}}_{ frac{pi}{6}} cosxdx=sinxbigg|^{ frac{pi}{2}}_{ frac{pi}{6}}=sin frac{pi}{2}-sin frac{pi}{6}=1-0,5=0,5$
$displaystyle 10) int^7_2 frac{dx}{x^2}=- frac{1}{x} big|^7_2=- frac{1}{7}+ frac{1}{2}= frac{5}{14}$
$displaystyle 22) int^{ frac{pi}{4}}_0 frac{dx}{cos^2x}=tgx bigg|^{ frac{pi}{4}}_0=tg frac{pi}{4}-tg0=1$
$displaystyle a) int^3_12xdx=x^2 big|^3_1=9-1=8$
$displaystyle b) int^4_1 (x^2-6x+9)dx= frac{x^3}{3}-3x^2+9x big|^4_1= frac{64}{3}-48+36-( frac{1}{3}-3+9)$
$displaystyle = frac{64}{3}-12- frac{1}{3}-6= frac{63}{3}-18=21-18=3$