if f(x+y)=f(x) +f(y) , x,yR and f^'(0) exists and  _{[ r=1]}^{[6 ]}  (r_{[ 0]}^{[6 ]} f(x)dx)=441 find f(x).

pls tell me how to solve such probs and the detailed solution.

well,the func. can be satisfied as:-

f(x) = kx

 

kx dx = kx²/2  for 0 to 6

           = 18k

now

r (18k) submission = (18k)6(6+1)/2

&it is equal to 441

=> k = 7/6

 

f(x) = 7x/6