Question

Aria zonei cuprinsa intre graficele functiilor f,g:[0,infinit), f(x)=(x^2)/6, g(x)=radical(6*x)

Answer 1

e   bine   sa   schtezi  grafic  cele   2   functii>
intersectezi cele  2   curbe
f(x)=g(x)
x²/6=√6x
x^4/36=6x   x1=0
x^3=36*6   x2=6
Compari   f(x(  cu  g(x(+
f(x)-g(x)=x^2/6-√6x=√x(x*√x/6-√6)
Pt   x∈[0,6] produsul  e   negativ  Deci  f(x)≤g(x0
Aria=∫[g(x)-f(x)]dx=∫g(x)dx-∫f(x)dx    x∈[0,6]
∫g(x)dx=∫√6xdx=√6∫√xdx=√6∫x^(1/2)dx=√6 x^(3/2):3/2=2√6x^(3/2)/3=conf   leibnitz Newton=2√6*6^3/2l3-0=2*6²/3=2812=24
∫f(x)dx=∫x²/6dx=   x∈[0,6]
1/6 x³/3=x³/18lo↑6=6³/18=12
aria=24-12=12
Aria  este  suprafata  innegrita   din figura,  cuprinsa  intre   graficele  celor   2   curbe