Question

найти интеграл.помогите пожалуйста​

Answer 1

Ответ:

1) -20

∫2x-3dx=∫2x dx-∫3dx=x^2-3x

2^2-3*2-((-3)^2-3*(-3))=4-6-18=20

2) -3.5

∫x-4/x^2dx

∫x dx-∫4/x^2dx

x^2/2+4/x

(-1)^2/2+4/-1-((-2)^2/2+4/-2)=1/2-4-(2-2)=1/2-4=-7/2=-3.5

3) 6.6

∫(3x+1)^3dx=∫t^3/3dt

1/3t^4/4=1/3*(3x-1)^4/4=(3x-1)^4/12

(3*2/3+1)^4/12-(3*0+1)^4/12=20/3=6.6

4) 31/35

∫(1-x)^4/7dx

1/7*∫(1-x)^4dx

1/7*∫-t^4dx=-1/7*t^5/5=-1/7*(1-x)^5/5=-(1-x)^5/35

-(1-0)^5/35-(-(1-(-1))^5/35)=31/35

5) 65/32

∫(2-x)^3/8dx1/8*∫(2-x)^3dx

1/8*∫-t^3dt

-1/8*t^4/4

-1/8*(2-x)^4/4=-(2-x)^4/32

-(2-4)^4/32-(-(-(1))^4/32)=65/32