Area Question 30
Question 30
- 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) $\int_{1}^{e} \ln y d y$
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Solution:
- Shaded area $=e-\int_{0}^{1} e^{x} d x=1$
Also, $\int_{1}^{e} \ln (e+1-y) d y \quad$ [put $e+1-y=t \Rightarrow \quad-d y=d t$ ]
$$ =\int_{e}^{1} \ln t(-d t)=\int_{1}^{e} \ln t d t=\int_{1}^{e} \ln y d y=1 $$
