#Assume f has a continuous second derivative. No idea where to even start with this
leaden path
placid ventureBOT
leaden path
Only need help with question 2, no idea where to even start with this
gilded egret
dire patrol
Consider the integral of f'(x) between a and b.
That integral is on one hand equal to f(b)-f(a).
On the other hand, integrate it by parts:
Set v = f'
u' = 1
And then take u = x-b
And therefore v' = f''
Therefore we have the integral of f' =
[(x-b) f'(x)] between a and b- integral ( f"(x)(x-b))
$f(b)-f(a) = \int_a^b f'(x)
= [(x-b)f'(x)]_a^b - \int_a^b f"(x)(x-b)$
grand cairnBOT
Daddy_314
leaden path
$f(b)-f(a) = \int_a^b f'(x)
= [(x-b)f'(x)]_a^b - \int_a^b f"(x)(x-b)$
Would this be the final answer? I’m not sure what kind of final answer I’m looking for, like I’m unsure of what the final result should look like or how to get there