Question

va eog eu mult!!!!!!!​

Answer 1

Răspuns:

Explicație pas cu pas:

a) ∫f(x)√(x-2) fx = ∫x(x-2)dx =∫(x^2 -2x)dx=x^3/3 -x^2

Punand limitele:

I = 3^3/3 -9 -(2^3/3 -2^2)= 9-9-8/3+4 = 4/3

b) g(x) = (x+2)√(x+2 -2)*√e^x/(x+2) = √(xe^x)

Vol = pi*∫g^2*dx = pi*∫xe^x dx=pi*(xe^x -e^x)

Punand limitele:

Vol= pi*((1*e^1 -e^1 -(0*e^0 -e^0)) = pi(0 -(-1)) = pi

c) f(t)*1/√(t-2) = t√(t-2)/√(t-2) = t

∫tdt = t^2/2

Punand limitele:
x^2/2 - 3^2/2 = (x^2 -9)/2

lim(x -> inf ;  ((x^2 -9)/2)/x^2) =

lim(x -> inf ; 1/2 - 9/(2x^2)) = 1/2 -0 = 1/2