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Question

# Statement-I: The value of the integral π/3∫π/6dx1+√tanx is equal to π6. Statement-II: b∫af(x)d(x)=b∫af(a+b−x)d(x).

A
Statement-I is true; Statement-II is true; Statement-II is a correct explanation for Statement-I.
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B
Statement-I is true; Statement-II is true; Statement-II is not a correct explanation for Statement-I.
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C
Statement-I is true; Statement-II is false.
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D
Statement-I is false; Statement-II is true.
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Solution

## The correct option is D Statement-I is false; Statement-II is true.I=π/3∫π/6dx1+√tanx...(1) =π/3∫π/6dx1+√tan(π3+π6−x) =π/3∫π/6dx1+√cotx =π/3∫π/6√tanx1+√tanxdx...(2) Adding (1) and (2) ⇒2I=π/3∫π/61+√tanx1+√tanxdx ⇒2I=π/3∫π/61dx ⇒2I=π6 ⇒I=π12 ∴ Statement-I is not true and Statement-II is the property So, Statement-II is always true

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