Home
Class 12
MATHS
Evaluate the integral int(pi//6)^(pi//3)...

Evaluate the integral `int_(pi//6)^(pi//3) (dx)/(1+sqrt(tanx))`

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`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise JEE ADVANCED|38 Videos

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise NUMERICAL VALUE_TYPE|28 Videos

  • CURVE TRACING

    CENGAGE ENGLISH|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

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

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

Evaluate int_(pi/6)^(pi/3)(dx)/(1+sqrt(tanx))

Evaluate: int_(pi/6)^(pi/3)(dx)/(1+sqrt(tanx))

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

int_(pi//6)^(pi//3) sin(3x)dx=

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

Evaluate of each of the following integral: int_(pi//6)^(pi//3)1/(1+sqrt(tanx))dx

Evaluate the following integral: int_(pi//3)^(pi//2)(sqrt(1+cosx))/((1-cosx)^(3//2))dx

Evaluate the definite integrals int_(pi/6)^(pi/3)(sinx+cosx)/(sqrt(sin2x))dx