Home
Class 12
MATHS
Evaluate the definite integral: int(-1/(...

Evaluate the definite integral: `int_(-1/(sqrt(3)))^(1/(sqrt(3)))((x^4)/(1-x^4))cos^(01)((2x)/(1+x^2))dxdot`

Text Solution

Verified by Experts

The correct Answer is:
`(pi)/(4) ln (2+sqrt(3))+(pi^(2))/(12)-(pi)/(sqrt(3))`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 3 Part - II|25 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

int_(-1/sqrt3)^(-1/sqrt3)(x^4)/(1-x^4)cos^(- 1)((2x)/(1+x^2))dx

Evaluate the definite integrals int_0^1 (dx)/(sqrt(1+x)-sqrt(x))

Evaluate the definite integrals int_0^1 (dx)/(sqrt(1+x)-sqrt(x))

Evaluate the following integral: int_0^(1//sqrt(3))tan^(-1)((3x-x^3)/(1-3x^2))dx

Evaluate the following definite integral: int_0^(1//2)1/(sqrt(1-x^2))dx

Evaluate the following definite integral: int_0^4 1/(sqrt(4x-x^2))dx

Evaluate the following definite integral: int_0^2 1/(sqrt(3+2x-x^2))dx

Evaluate the following integrals : int(x^(-1/3)+sqrt(x)+2)/(3sqrt(x)) dx

Evaluate the integral int(1)/(x^(3)sqrt(x-1))dx .

Evaluate the following definite integral: int_1^4(x^2+x)/(sqrt(2x+1))dx

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -High Level Problem
  1. Evaluate Lim(n->oo)n^2 int(-1/n)^(1/n) (2006sinx+2007cosx) |x|dx

    Text Solution

    |

  2. Find f(x) if it satisfies the relation f(x) = e^(x) + int(0)^(1) (x...

    Text Solution

    |

  3. Evaluate the definite integral: int(-1/(sqrt(3)))^(1/(sqrt(3)))((x^4)/...

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

  5. Prove that for any positive integer k ,(sin2k x)/(sinx)=2[cosx+cos3x+...

    Text Solution

    |

  6. If n gt 1. Evaluate int(0)^(oo)(dx)/((x+sqrt(1+x^(2)))^(n))

    Text Solution

    |

  7. Let f(x) be a continuous function AA xepsilonR, except at x=0, such th...

    Text Solution

    |

  8. Given that lim(nrarroo) sum(r=1)^(n) (log(e)(n^(2)+r^(2))-2log(e)n)/n ...

    Text Solution

    |

  9. Given that lim(x to 0)(int(0)^(x)(t^(2))/(sqrt(a+t))dt)/(bx-sinx) = 1,...

    Text Solution

    |

  10. Sketch the graph of cos^(-1)(4x^3-3x) and find the area enclosed betwe...

    Text Solution

    |

  11. Consider a square with vertices at (1, 1), (-1, 1), (-1, -1) and (1, -...

    Text Solution

    |

  12. Let [x] denotes the greatest integer function. Draw a rough sketch of ...

    Text Solution

    |

  13. Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x l...

    Text Solution

    |

  14. Find the area of region : {(x,y) : 0 le y le x^(2) + 1, 0 le y le x + ...

    Text Solution

    |

  15. A curve y=f(x) passes through point P(1,1) . The normal to the curv...

    Text Solution

    |

  16. Find the area of the region which contains all points satisfying condi...

    Text Solution

    |

  17. Find the area of the region which is inside the parabola y = - x^(2) +...

    Text Solution

    |

  18. Area bounded by the line y=x, curve y=f(x),(f(x)gtx,AA xgt1) and the l...

    Text Solution

    |

  19. Let C(1) and C(2) be the graphs of the functions y=x^(2) and y=2x, res...

    Text Solution

    |

  20. If [4a2 4a 1 4b2 4b 1 4c2 4c 1] [f-1 f1 f2] = [3a2 + 3a 3b2 + 3b 3c2 +...

    Text Solution

    |