turkey-yks 2015 Q45

turkey-yks · Other · lys1-math Integration by Parts Definite Integral Evaluation by Parts
For a function f defined on the set of real numbers and twice differentiable,
$$\begin{aligned} & f ( 1 ) = f ( 2 ) = 2 \\ & f ^ { \prime } ( 1 ) = f ^ { \prime } ( 2 ) = - 1 \end{aligned}$$
the following equalities are given.
Accordingly, what is the value of the integral $\int _ { 1 } ^ { 2 } x \cdot f ^ { \prime \prime } ( x ) d x$?
A) $- 1$
B) $- 2$
C) $- 3$
D) $\frac { - 1 } { 2 }$
E) $\frac { - 2 } { 3 }$
For a function f defined on the set of real numbers and twice differentiable,

$$\begin{aligned}
& f ( 1 ) = f ( 2 ) = 2 \\
& f ^ { \prime } ( 1 ) = f ^ { \prime } ( 2 ) = - 1
\end{aligned}$$

the following equalities are given.

Accordingly, what is the value of the integral $\int _ { 1 } ^ { 2 } x \cdot f ^ { \prime \prime } ( x ) d x$?\\
A) $- 1$\\
B) $- 2$\\
C) $- 3$\\
D) $\frac { - 1 } { 2 }$\\
E) $\frac { - 2 } { 3 }$