Home
Class 12
MATHS
f(x)=int1^x(tan^(-1)(t))/t dt \ AAx in ...

`f(x)=int_1^x(tan^(-1)(t))/t dt \ AAx in R^+,` then find the value of `f(e^2)-f(1/(e^2))`

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

If f(x)=int_(1)^(x)(log_(e)t)/(1+t)dt , where xgt0 , find the value of f(x)+f((1)/(x)) and hence show that, f(e)+f((1)/(e))=(1)/(2) .

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

If f'(x)=f(x)+ int_(0)^(1)f(x)dx , given f(0)=1 , then find the value of f(log_(e)2) is

If f(x)=min(|x|,1-|x|,1/4)AAx in R , then find the value of int_(-1)^1f(x)dxdot

Let f(x)=1/x^2 int_4^x (4t^2-2f'(t))dt then find the value of 9f'(4)

If int_(0)^(x) f(t)dt=x+int_(x)^(1)t f(t)dt , find the value of f(1).

Let f(x) be a differentiable function satisfying f(x)=int_(0)^(x)e^((2tx-t^(2)))cos(x-t)dt , then find the value of f''(0) .

Let f(x)=int_0^xe^t(t-1)(t-2)dt , Then f decreases in the interval

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

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

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. if [x] denotes the greatest integer less than or equal to x then integ...

    Text Solution

    |

  2. The value of int0^(2pi)[2sinx]dx ,w h e r e[dot] represents the great...

    Text Solution

    |

  3. f(x)=int1^x(tan^(-1)(t))/t dt \ AAx in R^+, then find the value of f...

    Text Solution

    |

  4. Let f be a positive function. Let I1=int(1-k)^k xf([x(1-x)])dx , ...

    Text Solution

    |

  5. Find the points of minima for f(x)=int0^x t(t-1)(t-2)dt

    Text Solution

    |

  6. Iff(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4), then find the value of ...

    Text Solution

    |

  7. If g(x)=int0^xcos^4tdt , then g(x+pi) equals (a)g(x)+g(pi) (b) g(...

    Text Solution

    |

  8. Evaluate lim(x to 4)int4^x((4t-f(t)))/((x-4))dt

    Text Solution

    |

  9. Evaluate: int(pi/4)^((3pi)/4)dx/(1+cosx)

    Text Solution

    |

  10. If In=int0^1(1-x^5)^n dx ,t h e n(55)/7(I(10))/(I(11))is equal to

    Text Solution

    |

  11. Let f be a one-to-one continuous function such that f(2)=3 and f(5)=7....

    Text Solution

    |

  12. The integral int(-1/2)^(1/2) ([x]+1n((1+x)/(1-x)))dx is equal to (wher...

    Text Solution

    |

  13. Evaluate: int0^(e-1)(e^((x^2+2x-1)/2))/(x+1)dx+int1^e xlogx e^(x^(2-2)...

    Text Solution

    |

  14. Evaluate lim(xrarr0)(x-int0^(x) cost^2dt)/(x^3-6x)

    Text Solution

    |

  15. The value of 2^(2010)(int0 ^1x^(1004)(1-x)^(1004)dx)/(int0^1x^(1004)(...

    Text Solution

    |

  16. If int(0)^(1)(e^(t))/(1+t)dt=a then find the value of int(0)^(1)(e^(t)...

    Text Solution

    |

  17. If f(x)=x+int0^1t(x+t)f(t)dt ,then the value of 23/2f(0) is equal...

    Text Solution

    |

  18. Let f:(0,oo)to(0,oo) be a differentiable function satisfying, int0^x(1...

    Text Solution

    |

  19. If f(x)a n dg(x) are continuous functions, then int(1nlambda)^(1n1/lam...

    Text Solution

    |

  20. The value of int-pi^pi cos^2x/[1+a^x]dx, a > 0 is

    Text Solution

    |