Home
Class 12
MATHS
Iff(x)=int1^x(logt)/(1+t+t^2)dxAAxlt=1,t...

`Iff(x)=int_1^x(logt)/(1+t+t^2)dxAAxlt=1,t h e np rov et h a tf(x)f(1/x)dot`

Text Solution

Verified by Experts

The correct Answer is:
NA
Given `f(x)=int_(1)(x)(logt)/(1+t+t^(2))dt`
or `f(1/x)=int_(1)^(1//x)(logt)/(1+t+t(2))dt`
Let `y=1/t` or `dy=(dt)/(t^(2))`
`:. f(1/x)=int_(1)^(x)("log"1/y)/(1+1/y+1/(y^(2)))(-1/(y^(2))dy)`
`=int_(1)^(x)(logy)/(1+y+y^(2))dy=f(x)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.11|6 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Single)|113 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.9|9 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

Ify=int_0^xf(t)sin{k(x-t)dt ,t h e np rov et h a t(dt^2y)/(dx^2)+k^2y=kf(x)dot

For x >0,l e tf(x)=int_1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/x) and find the value of f(e)+f(1/e)dot

Given I_m=int_1^e(logx)^mdx ,t h e np rov et h a t(I_m)/(1-m)+m I_(m-2)=e

IfI_n=int_0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)I_n+(n-1)I_(n-2)=-1/n+pi/2

If f(x)=int_(2)^(x)(dt)/(1+t^(4)) , then

If f(x+2a)=f(x-2a),t h e np rov et h a tf(x)i sp e r iod i cdot

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

If int_0^ycost^2dt=int_0^(x^2)(sint)/t dx ,t h ep rov et h a t(dy)/(dx)=(2sinx^2)/(xcosy^2)

Iff(x)=x+int_0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is equal to _________

If f(x)=1+1/x int_1^x f(t) dt, then the value of (e^-1) is