Question

The area bounded by y = x e^{| x |} and the lines | x | = 1, y = 0 is –

• A. 4
• B. 6
• C. 1
• D. 2

Answer 1

Answer: (D)

2

Answer 2

Since | x | = 1, x = ± 1

\ y = x e^{| x |} = $\left\{ \begin{matrix} xe^{- x}, & - 1 < x < 0 \\ xe^{x}, & 0 \leq x < 1 \end{matrix} \right.\$

\ Required area = $\left| \int_{–1}^{0}{xe^{- x}dx} \right|$ + $\left| \int_{0}^{1}{xe^{x}dx} \right|$

= $\left| \left\lbrack - xe^{- x} - e^{- x} \right\rbrack_{–1}^{0} \right|$ + $\left| \left\lbrack xe^{x} - e^{x} \right\rbrack_{0}^{1} \right|$

= | –1 – e + e| + |e – e – 0 + 1| = 2 sq. units.