Home
Class 12
MATHS
If the value of the definite integral in...

If the value of the definite integral `int_0^1(sin^(-1)sqrt(x))/(x^2-x+1)dx` is `(pi^2)/(sqrt(n))` (where `n in N),` then the value of `n/(27)` is

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

The value of the definite integral, int_0^(pi/2) (sin5x)/sinx dx is

The value of the definite integral int_(-1)^(1)(1+x)^(1//2)(1-x)^(3//2)dx equals

The value of the integral int_(0)^(1) x(1-x)^(n)dx is -

If the value of the definite integral int_0^1 "^(207)C_7x^(200)(1-x)^7dx is equal to 1/k ,w h e r ek in N , then the value of k/(26) is____

The value of the integral int(sin(x/2))/sqrt(1+sin(x/2)) dx can be

Integrate : int((xsin^(-1)x)/(sqrt(1-x^(2)))dx

The value of the integral int_0^(1/2)(1+sqrt(3))/(((x+1)^2(1-x)^6)^(1/4))dx is ______.

The value of the integral sqrt2 int_0^pi sqrt(1-cos2x) dx is ?

The value of the integral int_0^1sqrt((1-x)/(1+x))dx i s (a) pi/2+1 (b) pi/2-1 (c) -1 (d) 1

The value of the integral int_((1)/(n))^((an-1)/(n))(sqrt(x)dx)/(sqrt(a)-x+sqrt(x)) is -

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. If f^(prime)(x)=f(x)+int0^1f(x)dx ,gi v e nf(0)=1, then the value of ...

    Text Solution

    |

  2. STATEMENT 1: int0^pisqrt(1-sin^2x) dx=0 , STATEMENT 2: int0^picosx dx...

    Text Solution

    |

  3. STATEMENT 1: Let m be any integer. Then the value of Im=int0^pi(sin2m ...

    Text Solution

    |

  4. STATEMENT 1: inta^xf(t)dt is an even function if f(x) is an odd functi...

    Text Solution

    |

  5. STATEMENT 1: The value of int0^(2pi)cos^(99)x dx is 0 STATEMENT 2: in...

    Text Solution

    |

  6. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

    Text Solution

    |

  7. Let S be the area of the region enclosed by y=e^(-x^(2)),y=0, x=0 and ...

    Text Solution

    |

  8. Let f : (0,infty) rarr R be given by f(x) = int(1/x)^(x) e^-(t + 1/t...

    Text Solution

    |

  9. Show that int0^pixf(sinx)dx=pi/2int0^pif(sinx)dxdot

    Text Solution

    |

  10. Let f(x) be a non-constant twice differentiable function defined on (-...

    Text Solution

    |

  11. Let f(x)=int2^x(dt)/(sqrt(1+t^4))a n dg(x) be the inverse of f(x) . Th...

    Text Solution

    |

  12. Let f be a real-valued function defined on interval (0,oo),by f(x)=lnx...

    Text Solution

    |

  13. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

    Text Solution

    |

  14. If the value of the definite integral int0^1(sin^(-1)sqrt(x))/(x^2-x+1...

    Text Solution

    |

  15. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2, pi/2). T...

    Text Solution

    |

  16. The option(s) with the values of a and L that satisfy the following eq...

    Text Solution

    |

  17. Let f: R->R be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

    Text Solution

    |

  18. Prove that int0^1tan^(-1)(1/(1-x+x^2))dx=2int0^1tan^(-1)x dx. Hence ...

    Text Solution

    |

  19. Let f(x)=|[secx,cosx,sec^2x+cotxcos ecx],[cos^2x,cos^2x, cosec^2x],[1,...

    Text Solution

    |

  20. If f(x)=inta^x[f(x)]^(-1)dx and inta^1[f(x)]^(-1)dx=sqrt(2), then

    Text Solution

    |