Area Ques 40
Question
- Area of the region bounded by the curve $y=e^{x}$ and lines $x=0$ and $y=e$ is
(2009)
(a) $e-1$
(b) $\int _{1}^{e} \ln (e+1-y) d y$
(c) $e-\int _{0}^{1} e^{x} d x$
(d) $\int _{1}^{e} \ln y d y$
Show Answer
Answer:
Correct Answer: 40.(b,c,d)
Solution:
Formula:
- Shaded area $=e-(\int _{0}^{1} e^{x} d x)=1$
Also, $\int _{1}^{e} \ln (e+1-y) d y \quad$ [put $e+1-y=t \Rightarrow \quad-d y=d t$ ]
$ =\int _{e}^{1} \ln t(-d t)=\int _{1}^{e} \ln t d t=\int _{1}^{e} \ln y d y=1 $
BETA
