Can you help for this ?

14
0
Find all continuous functions f(x) satisfying
f(x)>1 and f(x) = x +(1 to x integral) [tex]\int[/tex] f(t).dt
for all x
 
Do you mean

[tex]f(x) = x + \int_{1}^{x} f(t) dt[/tex]

???
 
Hint: Show that f(x) has to be differentiable. Then differentiate both sides of the equation.
 
14
0
Hint: Show that f(x) has to be differentiable. Then differentiate both sides of the equation.
So i did it but how can i provide the result by this way
 
14
0
Do you mean

[tex]f(x) = x + \int_{1}^{x} f(t) dt[/tex]

???
Yes i mean this integral
 

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