csat-suneung 2012 Q16

csat-suneung · South-Korea · csat__math-science 4 marks Areas by integration

In the figure, let $a$ be the area of region $A$ enclosed by the two curves $y = e ^ { x } , y = x e ^ { x }$ and the $y$-axis, and let $b$ be the area of region $B$ enclosed by the two curves $y = e ^ { x } , y = x e ^ { x }$ and the line $x = 2$. What is the value of $b - a$? [4 points]
(1) $\frac { 3 } { 2 }$
(2) $e - 1$
(3) 2
(4) $\frac { 5 } { 2 }$
(5) $e$

In the figure, let $a$ be the area of region $A$ enclosed by the two curves $y = e ^ { x } , y = x e ^ { x }$ and the $y$-axis, and let $b$ be the area of region $B$ enclosed by the two curves $y = e ^ { x } , y = x e ^ { x }$ and the line $x = 2$. What is the value of $b - a$? [4 points]\\
(1) $\frac { 3 } { 2 }$\\
(2) $e - 1$\\
(3) 2\\
(4) $\frac { 5 } { 2 }$\\
(5) $e$

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