Definite Integration Question 455
Question: The area bounded by the straight lines $ x=0,x=2 $ and the curves $ y=2^{x},y=2x-x^{2} $ is
[AMU 2001]
Options:
A) $ \frac{4}{3}-\frac{1}{\log 2} $
B) $ \frac{3}{\log 2}+\frac{4}{3} $
C) $ \frac{4}{\log 2}-1 $
D) $ \frac{3}{\log 2}-\frac{4}{3} $
Show Answer
Answer:
Correct Answer: D
Solution:
Required area = $ \int_0^{2}{[2^{x}-(2x-x^{2})]dx} $
$ =[ \frac{2^{x}}{\log 2}-x^{2}+\frac{x^{3}}{3} ]_0^{2} $
$ =\frac{4}{\log 2}-4+\frac{8}{3}-\frac{1}{\log 2} $
$ =\frac{3}{\log 2}-\frac{4}{3} $ .
BETA
