Question

Integration by parts: Where f''(x) is a twice differentiable function, f(0)=1, f(1)=6, and f'(1)=5, evaluate the following integral.

Answer 1

$xf''(x)dx (on the interval 0 to 1)

Answer 2

If I understand it correctly, it becomes xf'(x)+xf'(1), but I am unsure where to go from there.

Answer 3

\[\large \int\limits_0^1 \color{royalblue}{x}\color{green}{f''(x)dx}\]
This is the integral yes?
It requires integration by parts, have you learned this process yet? :)

Answer 4

Yep! Which is how I got the above work; there is a third term but as it is f(0)*(0) it disappears.

Answer 5

I amk a little iffy on integration by parts, which is probably why I'm struggling with this question, ahahaha...

Answer 6

\[\large \color{royalblue}{u=x}\qquad \rightarrow \qquad \color{royalblue}{du=dx}\]\[\large \color{green}{dv=f''(x)dx}\qquad \rightarrow \qquad \color{green}{v=f'(x)}\]