C2 integration

Hey, I was wondering if someone could help me with this question. The answer to part (i) is k=4

In the second part i got 4/2root2 but the mark scheme says that it is wrong. In the mark scheme they change infinity to 4, but why?

What is the answer on the MS?

just root 2

If you mean you got $\dfrac{4}{2\sqrt{2}}$ then this is fine because it is equal to $\sqrt{2}$ which is the answer.

As for why they change to 4, I don't know. Post the mark scheme.

oh i feel like an idiot!! have they they just rationalised the denominator then?


also mark scheme

oh i feel like an idiot!! have they they just rationalised the denominator then?


also mark scheme

Yes.

Yes they rationalised the denominator.

What they do in MS is they turn the integral into a proper one with a limit of $k$ (which has a different value than in the prev part), then they evaluate the integral in terms of k, then they see what the limit of it is when $k \rightarrow \infty$.