Home
Class 12
MATHS
Ifint0^(f(x))t^2dt=xcospix ,t h e nf^(pr...

`Ifint_0^(f(x))t^2dt=xcospix ,t h e nf^(prime)(9)i s` `-1/9` (b) `-1/3` (c) `1/3` (d) non-existent

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)=(log)_x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e (c) 1 (d) zero

If f(x)=int_0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 (b) 1/2 (c) 1 (d) none of these

If f(x)=(log)_x(log x),t h e nf^(prime)(x) at x=e is equal to (a) 1/e (b) e (c) 1 (d) zero

If f(x)=cosx-int_0^x(x-t)f(t)dt ,t h e nf^(primeprime)(x)+f(x) is equal to (a) -cosx (b) -sinx (c) int_0^x(x-t)f(t)dt (d) 0

If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is (a) (sqrt(pi))/6 (b) -sqrt(pi//6) (c) 1//sqrt(6) (d) pi//sqrt(6)

If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2),t h e n(dy)/(dx) at x=1 is (a)2 (b) 1 (c) -2 (d) none of these

If int_0^xf(t) dt=x+int_x^1 tf(t)dt, then the value of f(1)

ifint(dx)/(x^2(x^n+1)^(((n-1)/n)) )=-[f(x)]^(1/n)+c ,t h e nf(x)i s (a) (1+x^n) (b) 1+x^(-1) (c) x^n+x^(-n) (d) none of these

ifint(dx)/(x^2(x^n+1)^(((n-1)/n))=-[f(x)]^(1/n)+c ,t h e nf(x)i s (1+x^n) (b) 1+x^(-1) x^n+x^(-n) (d) none of these

If intsqrt(1+sinx)f(x)dx=2/3(1+sinx)^(3/2)+c ,t h e nf(x)e q u a l cosx (b) sinx (c) tanx (d) 1

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. If f(x)=1+1/x int1^x f(t) dt, then the value of f(e^-1) is

    Text Solution

    |

  2. If int0^1e^ (-x^2) dx=a , then find the value of int0^1x^2e^ (-x^2) dx...

    Text Solution

    |

  3. Ifint0^(f(x))t^2dt=xcospix ,t h e nf^(prime)(9)i s -1/9 (b) -1/3 (c...

    Text Solution

    |

  4. IfIn=int0^pix^nsinx dx ,t h e n fin d t h e v a l u eof I5+20 I3dot

    Text Solution

    |

  5. The value of int0^1lim(n->oo)sum(k =0)^n(x^(k+2)2^k)/(k!)dx is: (a) e...

    Text Solution

    |

  6. If I(n)=int(0)^(pi/2) sin^(n)x dx, then show that I(n)=((n-1)/n)I(n-2)...

    Text Solution

    |

  7. If A=int0^1 x^(50)(2-2x)^(50)dx ,B=int0^1 x^(50)(1-x)^(50)dx , which ...

    Text Solution

    |

  8. If In=int0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI(n+1)=2^(-n...

    Text Solution

    |

  9. Given that f satisfies |f(u)-f(v)|lt=|u-v| for u and v in [a , b]dot T...

    Text Solution

    |

  10. IfIn=int0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)In+(n-1)I(n-2...

    Text Solution

    |

  11. IfI=int(-20pi)^(20pi)|sinx|[sinx]dx(w h e r e[dot] denotes the greate...

    Text Solution

    |

  12. IfIm=int1^x(logx)^mdx satisfies the relation (Im)=k-l I(m-1) then A)k...

    Text Solution

    |

  13. The value of the integral int0^1sqrt((1-x)/(1+x))dx i s (a)pi/2+1 (b...

    Text Solution

    |

  14. IfI(m , n)=int0^(pi/2)sin^m xcos^n xdx , Then show that I(m , n)=(m-1...

    Text Solution

    |

  15. Evaluate: int0^pi(xsin2xsin(pi/2cosx))/(2x-pi)dx

    Text Solution

    |

  16. If IK=int1^e(lnx)^kdx(k in I^+)dx(k in I^+), then find the value of...

    Text Solution

    |

  17. If int0^x {int0^u f(t) dt}du is equal to (a) int0^x (x-u) f(u)du ...

    Text Solution

    |

  18. Prove that: In=int0^oox^(2n+1) e^ (-x^2) dx=(n !)/2,n in N.

    Text Solution

    |

  19. Solve the following 2lt=|x-2|lt=5

    Text Solution

    |

  20. The value of the integral underset(-1)overset(3 )int ("tan"^(1)(x)/(...

    Text Solution

    |