Home
Class 12
MATHS
Evaluate int(0)^(pi//4)ln(1+tanx)dx...

Evaluate `int_(0)^(pi//4)ln(1+tanx)dx`

Text Solution

Verified by Experts

Let `I=int_(0)^(pi//4)log(1+tanx)dx=int_(0)^(pi//4)log[1+(1-tanx)/(1+tanx)]dx=int_90)^(pi//4)log2dx-int_(0)^(pi//4)-log(1+tanx)dx`
`=(pi)/(4)log2-I`
So, `I=(pi)/(8)log2`
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Competition level Questions|80 Videos

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Objective Type Questions (Only one answer)|70 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION - J)(ANKASH CHALLENGERS QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

Evaluate int_(0)^(pi//4)In(1+tanx)dx

Evaluate : int_(0)^(pi/2)log(tanx)dx

Evaluate : int_0^(pi/4)log(1+tanx)dx .

Evaluate : int_0^(pi/4)log(1+tanx)dxdot

8. int_0^(pi/4) log(1+tanx)dx

Evaluate int_(0)^(pi//4) log (1+tan theta)d theta

Evaluate int_(0)^(pi//4)(dx)/(1+sinx)

Evaluate : int_(pi/3)^(pi/4)(tanx+cotx)^2dx

Evaluate : int_(pi/3)^(pi/4)(tanx+cotx)^2dx

Evaluate: int_0^(pi//4)"log"(1+"t a n x")dx