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 \[=\left| \int_{0}^{2}{[{{2}^{x}}-2x+{{x}^{2}}]dx} \right|\] \[=\left| \left[ \frac{{{2}^{x}}}{\log \,2}-2.\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3} \right]_{0}^{2} \right|\] \[=\left| \frac{4}{\log \,2}-4+\frac{8}{3}-\frac{{{2}^{0}}}{\log \,2} \right|\] \[=\left| \frac{4}{\log \,2}-\frac{4}{3}-\frac{1}{\log \,2} \right|\] \[=\frac{3}{\log \,2}-\frac{4}{3}\]You need to login to perform this action.
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