Let f x = 7 tan 8 ⁡ x + 7 tan 6 ⁡ x - 3 tan 4 ⁡ x - 3 tan 2 ⁡ x   for all x…

1. $\underset{0}{\overset{\frac{\pi }{4}}{\int }}x f\left(x\right)dx=\frac{1}{12}$
2. $\underset{0}{\overset{\frac{\pi }{4}}{\int }} f\left(x\right)dx=0$
3. $\underset{0}{\overset{\frac{\pi }{4}}{\int }}x f\left(x\right)dx=\frac{1}{6}$
4. $\underset{0}{\overset{\frac{\pi }{4}}{\int }} f\left(x\right)dx=1$

Solution

Asked in: JEE Advanced 2015 (Paper 2)

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