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Let I(1) = int(0)^(pi/4)x^(2008)(tanx )^...

Let `I_(1) = int_(0)^(pi/4)x^(2008)(tanx )^(2008)dx, I_(2) = int_(0)^(pi/4) x ^(2009)(tan x)^(2009)dx , I_(3) = int_(0)^(pi/4) x^(2010)(tanx)^(2010)dx` then which one of the following inequalities hold good?

A

`I_(2)lt I_(3)lt I_(1)`

B

`I_(1)lt I_(2)lt I_(3)`

C

`I_(3)lt I_(1)lt I_(2)`

D

` I_(3)lt I_(2)lt I_(1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Integrand are ` I_3 lt I_2 lt I_1` in `(0, (pi)/(4))`.
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