Definitive integral question

C

Colin67

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Hello All

Some pointers/suggestions would be appreciated please to the attached question.

Q3 drew.jpg

I know the fact below
1666643128901.png
From the given integral you get the integral with limits given of (8-2x) =1/2 ,replaced the f(x) with -f(3-x) in other integral, used the above again and get -f(8-x) +1,but limits are different, some pointer/tips would be appreciated, I have done a fair amount of standard integration before but not come across questions like this, to be honest the above fact was new to me.

Thanks
 
I cannot think of any way to determine the value of the integral in question, which makes me think that the answer must be A. But if I were a teacher I'd expect something more than intuition. One way to prove that there is not enough information would be to find to different functions which both satisfy the conditions but give different answers for the final integral.
 
Thank you for taking the time to answer the question, as I said in the initial post this type of question is new to me so I assumed it was my lack of knowledge that meant I was not able to answer, I will try and look for counter-examples as you suggest.
 
Colin67 said:
... I will try and look for counter-examples as you suggest.
Click to expand...

It might be easier if you define f(x) as a piecewise function...
f(x) = -g(3-x) IF x < 3/2
f(x) = g(x) IF x ≥ 3/2

When you evaluate the two integrals you could write f(x) in terms of g(x) by splitting each integral into two parts
Would you even need to split them up?
 
Last edited:
Hi Cubist

My view is that if f(x) is a piecewise function it has be continuous and differentiable
 
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