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Definite Integration question

2015 · Shift 2 · Q34

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2015 · Shift 2 · Q34

Definite Integration question

2015 · Shift 2 · Q34

JEE AdvancedMathematicsDefinite IntegrationMultiple correct+4 / −1

Let

f\left( x \right) = 7{\tan ^8}x + 7{\tan ^6}x - 3{\tan ^4}x - 3{\tan ^2}x

for all

x \in \left( { - {\pi \over 2},{\pi \over 2}} \right).

Then the correct expression(s) is (are)

A
$\int\limits_0^{\pi /4} {xf\left( x \right)dx = {1 \over {12}}}$
B
$\int\limits_0^{\pi /4} {f\left( x \right)dx = 0}$
C
$\int\limits_0^{\pi /4} {xf\left( x \right)dx = {1 \over {6}}}$
D
$\int\limits_0^{\pi /4} {f\left( x \right)dx = 1}$

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