Menu Close

please-solve-0-f-x-dx-g-x-




Question Number 8798 by javawithfish last updated on 28/Oct/16
please solve  ∫_0 ^∞ f(x)dx=g(x)
pleasesolve0f(x)dx=g(x)
Commented by Yozzias last updated on 28/Oct/16
Impossible unless g(x)=f(x)=0 ∀x∈R. The definite   integral ∫_a ^b f(x)dx gives a real number iff f is  integrable on [a,b]. We can say then that  ∫_a ^( b) f(x)dx is a function h of the real variables  a and b. ∴ h(a,b)=∫_a ^( b) f(x)dx (b≥a, (a,b)∈R^2 )  h cannot be a function of x therefore. Similarly  ∫_0 ^( ∞) f(x)dx cannot be a function of x itself  unless f(x)=0 ∀x∈R.
Impossibleunlessg(x)=f(x)=0xR.Thedefiniteintegralabf(x)dxgivesarealnumberifffisintegrableon[a,b].Wecansaythenthatabf(x)dxisafunctionhoftherealvariablesaandb.h(a,b)=abf(x)dx(ba,(a,b)R2)hcannotbeafunctionofxtherefore.Similarly0f(x)dxcannotbeafunctionofxitselfunlessf(x)=0xR.
Commented by javawithfish last updated on 28/Oct/16
then the question must br lim_(x→∞) ∫_0 ^( x) f(x)dx=g(p)
thenthequestionmustbrlimx0xf(x)dx=g(p)

Leave a Reply

Your email address will not be published. Required fields are marked *