A) \[\frac{2}{\log 2}-\frac{4}{3}\]
B) \[\frac{3}{\log 2}-\frac{4}{3}\]
C) \[\frac{1}{\log 2}-\frac{4}{3}\]
D) \[\frac{4}{\log 2}-\frac{3}{2}\]
Correct Answer: B
Solution :
Required area \[=\int_{0}^{2}{[{{2}^{x}}-(2x-{{x}^{2}})]\,dx}\] \[=\int_{0}^{2}{({{2}^{x}}-2x+{{x}^{2}})\,dx}\] \[=\left[ \frac{{{2}^{x}}}{\log 2}-{{x}^{2}}+\frac{{{x}^{3}}}{3} \right]_{0}^{2}\] \[=\frac{4}{\log 2}-4+\frac{8}{3}-\frac{1}{\log 2}\] \[=\left( \frac{3}{\log 2}-\frac{4}{3} \right)\text{sq}\,\text{unit}\]You need to login to perform this action.
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