- #1
himanshu121
- 653
- 1
[tex] f(x)=x^2+\int_0^x e^{-t}f(x-t)dt[/tex] ...(I)
Find f(x)
Okay what i did:
For
[tex]\int_0^x e^{-t}f(x-t)dt[/tex]
I substituted h=x-t =>dh=-dt
so [tex]\int_0^x e^{h-x}f(h)dh[/tex]
Now i differentiated (I)
so i got
f'(x)=2x+f(x) after solvin this by integrating factor method i got different results which involve ex
But i had to prove f(x)=x2+x3/3
Find f(x)
Okay what i did:
For
[tex]\int_0^x e^{-t}f(x-t)dt[/tex]
I substituted h=x-t =>dh=-dt
so [tex]\int_0^x e^{h-x}f(h)dh[/tex]
Now i differentiated (I)
so i got
f'(x)=2x+f(x) after solvin this by integrating factor method i got different results which involve ex
But i had to prove f(x)=x2+x3/3