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in the question number 13 is an integration question, i am curious to know if there is a similar kind of questions like that that doesn't state the equation but only uses f(x), do you guys know what to search on the internet to find similar questions? and what methods can i use to solve it

Godlixe
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  • I believe these are called recursive functions, though I may be wrong. – Vishu Apr 02 '20 at 11:46
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    Observe that if you take the derivative then the integral goes away. (This doesn't always happen, here it happened because the integral in the integral equation had constant limits). Now solve the differential equation that you get from that, then plug it back into the integral equation to find the constant of integration. – Ian Apr 02 '20 at 11:47
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    In general this is an integral equation, but you may get rather overwhelmed if you try to look that up in general. – Ian Apr 02 '20 at 11:47
  • i still can't figure out how the answer is -1, all i get is (3x-f(x))/2 – Godlixe Apr 02 '20 at 12:27
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    $f'(x)=3$ so $f(x)=3x+C$, then $3x+C=3x+2\int_0^1 3t+C dt=3x+3+2C$, solve that equation for $C$, then you can just integrate normally. (Note that the question used sloppy notation by using the same variable name inside and outside of the integral sign.) – Ian Apr 02 '20 at 13:24
  • thank you very much @Ian – Godlixe Apr 02 '20 at 13:40

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