# Integration question

1. Jan 22, 2005

### trap

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).

Last edited: Jan 23, 2005
2. Jan 23, 2005

### Tide

Are you sure you copied the question correctly?

3. Jan 23, 2005

### trap

does it seem right now?

4. Jan 23, 2005

### marlon

Shouldn't it be f² in the solution in stead of f" ???

i mean the integrand is f * df/dt * dt right? so you have f * df as integrand

marlon

5. Jan 23, 2005

### dextercioby

1.DO NOT DOUBLE POST!!!!!!!!!!!

2.It's definitely
$$f^{2}(t)$$

The hint is good.I guess u needed us to tell u that u didn't copy the exercise properly. :tongue2:

Daniel.

6. Jan 23, 2005

### trap

yes, you are right marlon, my bad all the way