Question regarding IBP (1 Viewer)

[Paradoxica]

Has there ever been a HSC question where the student was required to use Integration By Parts more than twice?

 

[jonathan_lam]

Isn't that called reduction formula?

 

[Ekman]

I believe this has been asked before:

 

[Drsoccerball]

And also theres questions like You use it twice.

 

[Drsoccerball]

I believe this has been asked before:

lol

 

[jonathan_lam]

and and are also examples. Whether they have been asked before, I'm not too sure. I can't be bothered checking through all the past papers.

 

[RealiseNothing]

Guys he said more than twice.

 

[Carrotsticks]

If you mean using IBP more than twice on a single integral, I do not think so. The reason why we use integration by parts twice for some problems is often to take advantage of the fact that when the sinusoids get differentiated twice, they become the same thing (ignoring constants). For example 2003 HSC Question 8 or the classic integral of the exponential function multiplied by a sinusoid.

However, if you meant more than twice in a single proof, then there have been plenty. If I recall correctly, in 2010 HSC throughout Q8 you were required to use IBP four or five times in total.