csat-suneung 2016 Q20

csat-suneung · South-Korea · csat__math-A 4 marks Integration by Parts Definite Integral Evaluation by Parts
Two polynomial functions $f ( x ) , g ( x )$ satisfy for all real numbers $x$ $$f ( - x ) = - f ( x ) , \quad g ( - x ) = g ( x )$$ For the function $h ( x ) = f ( x ) g ( x )$, $$\int _ { - 3 } ^ { 3 } ( x + 5 ) h ^ { \prime } ( x ) d x = 10$$ What is the value of $h ( 3 )$? [4 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
Two polynomial functions $f ( x ) , g ( x )$ satisfy for all real numbers $x$
$$f ( - x ) = - f ( x ) , \quad g ( - x ) = g ( x )$$
For the function $h ( x ) = f ( x ) g ( x )$,
$$\int _ { - 3 } ^ { 3 } ( x + 5 ) h ^ { \prime } ( x ) d x = 10$$
What is the value of $h ( 3 )$? [4 points]\\
(1) 1\\
(2) 2\\
(3) 3\\
(4) 4\\
(5) 5