Home
Class 12
MATHS
Prove that: int(-a)^(a) log ((2-x)/(2+x)...

Prove that: `int_(-a)^(a) log ((2-x)/(2+x)) dx=0`

Text Solution

AI Generated Solution

To prove that \[ \int_{-a}^{a} \log\left(\frac{2-x}{2+x}\right) dx = 0, \] we will analyze the function inside the integral and determine whether it is odd or even. ...
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7a|14 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7b|26 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

Evaluate int_(-1)^(1) log ((2-x)/( 2+x)) dx

Prove that : int_(0)^(oo) log (x+(1)/(x)). (dx)/(1+x^(2)) = pi log_(e) 2

Prove that int_- 1^1log((2-x)/(2+x))^(20)dx=0

Prove that : int_(0)^(1) (log x)/(sqrt(1-x^(2)))dx=-(pi)/(2)log 2

Prove that: int_(-a)^(a) x^(3) sqrt(a^(2) -x^(2) ) dx=0

Prove that: int_(0)^(pi//2) log (sin x) dx =int_(0)^(pi//2) log (cos x) dx =(-pi)/(2) log 2

Prove that : int_(0)^(1)(sin^(-1)x)/(x) dx = (pi)/(2) log 2

int_(0)^(1)x log (1+2 x)dx

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

Prove that int_(0)^(oo) (sin^(2)x)/(x^(2))dx=int_(0)^(oo) (sinx)x dx