Thread: integration by parts problem

Suppose that f(x) and g(x) are functions with f(0)=g(0)=0, f(1)=g(1)=0, and with continuous second derivatives.

Use integration by parts to show that



Then come up with specific examples for f(x) and g(x) that satisfy the above.

I tried using
u=g(x) v=f(x)
du=g'(x)dx dv=f''(x)dx

then

u=g'(x) v=f(x)
du=g''(x)dx dv=f'(x)dx

but I ended up with



and I don't know how to get rid of the two middle functions...

if I switched what U was for the second time I applied it, I get back to where I began and If I apply IBP again, i get into 3rd derivatives...

I'm really confused. Can someone give me some advice?

Originally Posted by valkyrie

Suppose that f(x) and g(x) are functions with f(0)=g(0)=0, f(1)=g(1)=0, and with continuous second derivatives.

Use integration by parts to show that



Then come up with specific examples for f(x) and g(x) that satisfy the above.

I tried using
u=g(x) v=f(x)
du=g'(x)dx dv=f''(x)dx

then

u=g'(x) v=f(x)
du=g''(x)dx dv=f'(x)dx

but I ended up with



and I don't know how to get rid of the two middle functions...

if I switched what U was for the second time I applied it, I get back to where I began and If I apply IBP again, i get into 3rd derivatives...

I'm really confused. Can someone give me some advice?

I am guessing that the integrals have limits of integration, and the they are from 0 to 1 or the statement is not true.

dont forget to evaluate the middle parts and the conditions that f and g are = 0 at 1 and 0 will make them go away.

Hmmm, thanks. they are from 0 to 1 but I couldnt get the BB code to work properly!

I don't really remember in such an abstract situation... how do I evaluate the middle parts? do I just set them from 0 to 1?

Originally Posted by valkyrie

Hmmm, thanks. they are from 0 to 1 but I couldnt get the BB code to work properly!

I don't really remember in such an abstract situation... how do I evaluate the middle parts? do I just set them from 0 to 1?

but since



This is what we wanted yay

Originally Posted by TheEmptySet

but since



This is what we wanted yay

OH. wow. okay thank you that makes A LOT of sense. I was having an idiot moment.