Definite Integration Question 161
Question: What is the area bounded by the curves $ y=e^{x},y={e^{-x}} $ and the straight line $ x=1 $ -
Options:
A) $ ( e+\frac{1}{e} ) $ sq. unit
B) $ ( e-\frac{1}{e} ) $ sq. unit
C) $ ( e+\frac{1}{e}-2 ) $ sq. unit
D) $ ( e-\frac{1}{e}-2 ) $ sq. unit
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Given equations of curves are $ y=e^{x} $ and $ y={e^{-x}} $ .
$ \Rightarrow e^{x}=\frac{1}{e^{x}}\Rightarrow e^{2x}=e^{0}\Rightarrow x=0 $ Also, equation of straight line gives $ x=1 $
$ \therefore $ Required area $ =\int\limits_0^{1}{(e^{x}-{e^{-x}})dx} $
$ =[ e^{x}+{e^{-x}} ]_0^{1}=e+{e^{-1}}-e^{0}+{e^{-0}} $
$ =( e+\frac{1}{e}-2 ) $ sq unit
BETA
