- #1
mooncrater
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Homework Statement
The question says:
f (x)=x2+7x +∫0x(e-tf (x-t)dt.
Find f (x).
Homework Equations
None
The Attempt at a Solution
What I did is:
Consider the integral:
I=∫0x (e-tf (x-t)dt
We know that ∫abf (x)dx=∫abf (a+b-x)dc
So using it here:
1/ex∫0xetf (t)dt----(1)
Leaving the "1/ex part for now.
From the original equation f (t)=t2+7t +∫0te-t f (0)dt
And we can see that f (0)=0
So f (t)=t2+7t
Using (1) without 1/ex...
∫0xet(t2+7t)dt
Which can be calculated to ex(x2+5x -5)
Which is when divided by ex becomes
x2+5x-5=I
Now adding I to the original equation of f (x)..
Thus f (x)= 2x2+12x -5x.
But in the solution they have done something else. So what is wrong with my solution to this question?