Home
Class 12
MATHS
Let alpha & beta be distinct positive ro...

Let `alpha` & `beta` be distinct positive roots of the equation `tanx = 2x`, then evaluate `int_(0)^(1)sin(alphax).sin(betax) dx`

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 3 Part - II|25 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

  • DPP

    RESONANCE|Exercise QUESTION|665 Videos

Similar Questions

Explore conceptually related problems

Let alpha,beta be the distinct positive roots of the equation tan x=2x then evaluate int_(0)^(1)sin alpha x.sin beta xdx independent of alpha and beta

int(dx)/(sin(x-alpha)sin(x-beta))

Evaluate :int_(0)^( pi)(x)/(1+sin alpha sin x)dx

Let alpha, and beta are the roots of the equation x^(2)+x +1 =0 then

If alpha, beta in C are the distinct roots of the equation x^(2)-x+1=0 , then alpha^(101)+beta^(107) is equal to

If alpha,beta in C are distinct roots of the equation x^(2)+1=0 then alpha^(101)+beta^(107) is equal to

If alpha and beta are two distinct roots of the equation a cos x+b sin x=10, then tan((alpha+beta)/(2)) is equal to

tan alpha and tan beta are roots of the equation x^(2)+ax+b=0, then the value of sin^(2)(alpha+beta)+a sin(alpha+beta)cos(alpha+beta)+b cos^(2)(alpha+beta) is equal to

tan alpha and tan beta are roots of the equation x^(2)+ax+b=0, then the value of sin^(2)(alpha+beta)+a sin(alpha+beta)*cos(alpha+beta)+b cos^(2)(alpha+beta) is equal to

Let alpha , beta be the roots of the equation (x-a) (x-b) = c , cne 0 , then find the roots of the equation (x - alpha) (x -beta) + c = 0

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -High Level Problem
  1. Find the integral value of a for which int(0)^(pi//2)(sinx+acosx)^(3) ...

    Text Solution

    |

  2. Evaluate int(0)^(pi)sqrt((cosx+cos2x+cos3x)^(2)+(sinx+sin2x+sin3x)^(...

    Text Solution

    |

  3. Let alpha & beta be distinct positive roots of the equation tanx = 2x,...

    Text Solution

    |

  4. Evaluate : lim(ararr(pi/2)^(-)) int(0)^(a)(cosx)ln(cosx)dx

    Text Solution

    |

  5. Find the value of a(0 lt a lt 1) for which the following definite inte...

    Text Solution

    |

  6. Find the Lim(nrarroo) ((""^(3n)C(n))/(""^(2n)C(n)))^(1/n) Where ""^(...

    Text Solution

    |

  7. int0^oof(a/x+x/a)*(lnx)/x d x=lna*int(a/x+x/a)*(dx)/x

    Text Solution

    |

  8. Evaluate Lim(n->oo)n^2 int(-1/n)^(1/n) (2006sinx+2007cosx) |x|dx

    Text Solution

    |

  9. Let sequence (a(n)) be defined as a(1) = pi/4, a(n) = int(0)^(1//...

    Text Solution

    |

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

    Text Solution

    |

  11. Evaluate : int(-1//sqrt(3))^(1//sqrt(3))(x^(4))/(1-x^(4)) cos^(-1) ((2...

    Text Solution

    |

  12. Evaluate int(0)^(1)(1)/((5+2x-2x^(2))(1+e^((2-4x)))dx

    Text Solution

    |

  13. Prove that for any positive integer k , (sin2kx)/(sinx) = 2 [cosx+co...

    Text Solution

    |

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

    Text Solution

    |

  15. Let f(x) be a continuous function AAx in R , except at x=0, such that...

    Text Solution

    |

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

    Text Solution

    |

  17. For a natural the following questions : Now answer the following que...

    Text Solution

    |

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

    Text Solution

    |

  19. Draw a graph of the function f(x) = cos^(-1) (4x^(3)-3x), x in [-1,1] ...

    Text Solution

    |

  20. Consider a square with vertices at (1,1),(-1,1),(-1,-1),a n d(1,-1)dot...

    Text Solution

    |