Home
Class 12
MATHS
Statement-1: The value of the integral ...

Statement-1: The value of the integral
`int_(pi//6)^(pi//3) (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.
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Exercise|147 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test 1|60 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|145 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

The value of the integral int_(pi//6)^(pi//3) (1)/(1+sqrt(tan x))dx is

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

The value of the integral int_(pi//6)^(pi//3)(dx)/(1+tan^(5)x) is

Statement I The value of the integral int_(pi//6)^(pi//3) (dx)/(1+sqrt(tan x)) is pi/6 Statement II int_(a)^(b) f(x) dx = int_(a)^(b) f(a+b-x)dx

int_(pi//6)^(pi//3)(1)/(1+tan x) dx=

Statement 1: The value of the integral int_(pi//6)^(pi//3)(dx)/(1+sqrt(tanx)) is equal to pi/6 Statement 2: int_a^bf(x)dx=int_a^bf(a+b-x)dxdot Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true; Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

The value of the integral int_(pi//6)^(pi//2)((sinx-xcosx))/(x(x+sinx))dx is equal to