csat-suneung 2022 Q20

csat-suneung · South-Korea · csat__math 4 marks Indefinite & Definite Integrals Definite Integral Evaluation (Computational)

A function $f ( x )$ differentiable on the entire set of real numbers satisfies the following conditions.
(a) On the closed interval $[ 0,1 ]$, $f ( x ) = x$.
(b) For some constants $a , b$, on the interval $[ 0 , \infty )$, $f ( x + 1 ) - x f ( x ) = a x + b$. Find the value of $60 \times \int _ { 1 } ^ { 2 } f ( x ) d x$. [4 points]

A function $f ( x )$ differentiable on the entire set of real numbers satisfies the following conditions.\\
(a) On the closed interval $[ 0,1 ]$, $f ( x ) = x$.\\
(b) For some constants $a , b$, on the interval $[ 0 , \infty )$, $f ( x + 1 ) - x f ( x ) = a x + b$.\\
Find the value of $60 \times \int _ { 1 } ^ { 2 } f ( x ) d x$. [4 points]

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