# Integration question

1. Jan 23, 2005

### trap

I'm having major trouble with this question, can anyone assist me on this?

Let f be a function such that f' is continuous on [a,b]. Show that

$$\int_a^{b}$$ f(t)f’(t) dt = 1/2 [f''(b) - f''(a)]

Hint: Calculate the derivative of F(x) = f''(x).

2. Jan 23, 2005

### Zurtex

3. Jan 23, 2005

### trap

sorry, i thought a different forum would make a difference, since no one has an answer to my question yet.

4. Jan 23, 2005

### Zurtex

5. Jan 23, 2005

### shmoe

Hi, are you sure those are second derivatives on the right hand side and not squares? Something like $$1/2(f(b)^2-f(a)^2)$$ instead?

6. Jan 23, 2005

### trap

i'm not sure if they are squares becoz the question reads f^2(b) - f^2(a)..so i thought they were second derivative..

7. Jan 23, 2005

### Zurtex

That is squares and I am sure about that because it is the answer. When your talking about the nth derivative you either use roman numerals or put the number in brackets.

8. Jan 23, 2005

Couldn't one simply integrate by parts to get the answer?

9. Jan 24, 2005

### digink

Could you please explain how you come to that answer, I am having trouble seeing it.

Thanks.

10. Jan 24, 2005

### shmoe

Just use the hint applied to $$F(x)=(f(x))^2$$. Find the derivative of F(x) using the chain rule...

DeadWolfe-yes integration by parts will work fine.