A) \[\frac{7}{120}\]
B) \[\frac{9}{120}\]
C) \[\frac{11}{120}\]
D) \[\frac{13}{120}\]
Correct Answer: A
Solution :
The graph of \[y=2{{x}^{4}}-{{x}^{2}}\] is shown below: |
Minimum occurs at \[x=\pm \frac{1}{2}\] |
\[\therefore \]Desired area |
\[=2\int\limits_{0}^{1/2}{\left( -y \right)dx=2\int\limits_{0}^{1/2}{\left( {{x}^{2}}-2{{x}^{4}} \right)}dx}\] |
\[=2\left[ \frac{{{x}^{3}}}{3}-\frac{2{{x}^{5}}}{5} \right]_{0}^{1/2}=2\left[ \frac{1}{24}-\frac{1}{80} \right]=\frac{7}{120}\] |
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