Integrate f(t)f'(t) on [a,b] and Show 1/2[f''(b)-f''(a)]

[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).

 

[Tide]

Are you sure you copied the question correctly?

 

[trap]

does it seem right now?

 

[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

 

[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.

Daniel.

 

[trap]

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