A) \[f(4)f(2)\]
B) \[f(4)\]
C) \[f(2)\]
D) \[0\]
E) \[1\]
Correct Answer: E
Solution :
It is given that \[f(2)=\tan \frac{\pi }{4}=1,\]\[f(4)=\tan \frac{\pi }{3}=\sqrt{3}\] \[\therefore \]\[\int_{2}^{4}{f(x)f(x)}\,dx=\left[ \frac{1}{2}{{[f(x)]}^{2}} \right]_{2}^{4}\] \[=\frac{1}{2}{{[f(4)]}^{2}}-\frac{1}{2}{{[f(2)]}^{2}}\] \[=\frac{3}{2}-\frac{1}{2}=1\]You need to login to perform this action.
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