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Statement-1: The value of the integral ...

Statement-1: The value of the integral
`int_(pi//6)^(pi//3) (1)/(1+sqrt(tan)x)dx` is equal to `(pi)/(6)`
Statement-2: `int_(a)^(b) f(x)dx=int_(a)^(b) f(a+b-x)dx`

A

Statement-1 is true, Statement-2 is True,Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Text Solution

Verified by Experts

The correct Answer is:
D
Clearly, statement-2, being a standard property, is true.
We know that `underset(a)overset(b)int (f(x))/(f(x)+f(a+b-x))dx=(b-a)/(2)`
`:.underset(pi//6)overset(pi//3)int (1)/(1+sqrt(tanx))dx=underset(pi//6)overset(pi//2)int (sqrt(cos)x)/(sqrt(cos)x+sqrt(sin)x)dx=(1)/(2)((pi)/(3)-(pi)/(6))=(pi)/(12)`
So, statement-1 is not true.
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