Question

РЕШИТЕ ПОЖАЛУЙСТА........................

Answer 1

1
F(x)=x³/3+3x²+x+C
F(x)=4x²-x^7/7+C
2
F(x)=5x-2x³/3+C
-8=-15+18+C
c=-8-3=-11
F(x)=5x-2x³/3-11
3
F(x)=2x-3x³+C
f(3)=6-81+C=-75+C
-75+C<0
C<75
c∈(-∞;75)
F(x)=2x-3x³+3-например
4
$S= intlimits {(x^2-4x+2)} , dx =x^3/3-2x^2+2x|-1-(-3)=$$-1/3-2-2+9+18+6=$28 2/3

Answer 2

$1. intlimits { x^{2} +6x+1} , dx = frac{ x^{3} }{3}+ frac{ 6x^{2} }{2} + x +const = frac{ x^{3} }{3}+3 x^{2} +x+const intlimits {8x- x^{6} } , dx = frac{8 x^{2} }{2}- frac{ x^{7} }{7}+const = 4 x^{2} - frac{ x^{7} }{7}+const$

$2. intlimits {5-2 x^{2} } , dx = 5x- frac{2 x^{3} }{3}+const$
$(-3;-8): 5(-3)-2 (-3)^{2}+const=-8 -15+18+const = -8 const = -11$
$F(x) = 5x- frac{2 x^{3} }{3} - 11$

$3. intlimits {2-9 x^{2} } , dx = 2x-3 x^{3} + const$
$F(3) = 2*3 - 3*3^3 + const textless 0 6-81+const textless 0 const textless 75$
$F(x) = 2x - 3 x^{3} + 74$

$4. intlimits^{-1}_{-3} { x^{2} -4x+2} , dx = (frac{ x^{3} }{3}-2 x^{2} +2x) = ( frac{-1}{3}-2-2 ) - ( -9 - 18 -6 )$
$= - frac{1}{3} - 4 + 33 = 28 frac{2}{3}$