Gegeben §
f(x)=exg(x)=−2x+1
M={(x,y)∣0≤y≤min(f(x),g(x))}
Skizze §
Flächeninhalt §
A=∫−∞0exdx+∫02−2x+1dx
∫−∞0exdx=r→−∞lim∫r0exdx=r→−∞lim[ex]r0=r→−∞lim(e0−er)=1−x→∞limex1=1−0=1
∫02−2x+1dx=[−21⋅21x2+x]02=(−41⋅22+2)−0=1
A=1+1=2