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
