Definite Integration Question 165
Question: Which of the following is not the area of the region bounded by $ y=e^{x} $ and $ x=0 $ and y = e-
Options:
A) $ e-1 $
B) $ \int\limits_1^{e}{ln(e+1-y)dy} $
C) $ e-\int\limits_0^{1}{e^{x}dx} $
D) $ \int\limits_1^{e}{lnydy} $
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Answer:
Correct Answer: C
Solution:
[c] Required area $ =\int\limits_1^{e}{lnydy} $
$ =(ylny-y)_1^{e}=(e-e)-[-1]=1 $
Also, $ \int\limits_1^{e}{lnydy=\int\limits_1^{e}{ln(e+1-y)dy}} $ Further, required area $ =e\times 1-\int\limits_0^{1}{e^{x}dx} $
BETA
