[tex] f(x)=x^2+\int_0^x e^{-t}f(x-t)dt[/tex] ........(I)(adsbygoogle = window.adsbygoogle || []).push({});

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 e^{x}

But i had to prove f(x)=x^{2}+x^{3}/3

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Definite Integration

**Physics Forums | Science Articles, Homework Help, Discussion**