csat-suneung 2016 Q13

csat-suneung · South-Korea · csat__math-A 3 marks Areas by integration

For a natural number $n$, let P be the point with coordinates $( 0,2 n + 1 )$, and let Q be the point on the graph of the function $f ( x ) = n x ^ { 2 }$ with $y$-coordinate 1 in the first quadrant. When $n = 1$, what is the area of the region enclosed by the line segment PQ, the curve $y = f ( x )$, and the $y$-axis? [3 points]
(1) $\frac { 3 } { 2 }$
(2) $\frac { 19 } { 12 }$
(3) $\frac { 5 } { 3 }$
(4) $\frac { 7 } { 4 }$
(5) $\frac { 11 } { 6 }$

For a natural number $n$, let P be the point with coordinates $( 0,2 n + 1 )$, and let Q be the point on the graph of the function $f ( x ) = n x ^ { 2 }$ with $y$-coordinate 1 in the first quadrant.\\
When $n = 1$, what is the area of the region enclosed by the line segment PQ, the curve $y = f ( x )$, and the $y$-axis? [3 points]\\
(1) $\frac { 3 } { 2 }$\\
(2) $\frac { 19 } { 12 }$\\
(3) $\frac { 5 } { 3 }$\\
(4) $\frac { 7 } { 4 }$\\
(5) $\frac { 11 } { 6 }$

Paper Questions

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