[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

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# Definite Integration

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