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Statement I: The value of the integral i...

Statement I: The value of the integral `int_(pi//6)^(pi//3) (dx)/(1+sqrt(tanx))` is equal to `(pi)/6`.
Statement II: `int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx`

A

Statement I is true, statement II is true, statement II is a correct explanation for statement I

B

Statement I is true, statement II is true, statement II is a not a correct explanation for statement I

C

Statement I is true, statement II is false

D

Statement I is false, statement II is true

Text Solution

Verified by Experts

The correct Answer is:
D
`I=int_(pi//6)^(pi//3) (dx)/(1+sqrt(tanx))`………..i
`I=int_(pi//6)^(pi//3) (dx)/(1+sqrt(cotx))=int_(pi//6)^(pi//3)(sqrt(tanx)dx)/(sqrt(tanx)+1)`………..ii
Adding i and ii
`implies2I=int_(pi//6)^(pi//3) 1 dximplies2I=(pi)/3-(pi)/6`
`implies2I=(pi)/6impliesI=(pi)/12`
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