Home
Class 12
MATHS
IfAn=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,b...

`IfA_n=int_0^(pi/2)(sin(2n-1)x)/(sinx)dx ,b_n=int_0^(pi/2)((sinn x)/(sinx))^2dxforn in N ,` Then (a) `A_(n+1)=A_n` (b) `B_(n+1)=B_n` (c) `A_(n+1)-A_n=B_(n+1)` (d) `B_(n+1)-B_n=A_(n+1)`

A

`A_(n+1)=-A_(n)`

B

`B_(n+1)=B_(n)`

C

`A_(n+1)-A_(n)=B_(n+1)`

D

`B_(n+1)-B_(n)=A_(n+1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|64 Videos

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos

  • FUNCTIONS

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos

  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

Similar Questions

Explore conceptually related problems

If A_n=int_0^(pi/2)(sin(2n-1)x)/(sinx)dx ,B_n=int_0^(pi/2)((sinn x)/(sinx))^2 dx for n inN , Then (A) A_(n+1)=A_n (B) B_(n+1)=B_n (C) A_(n+1)-A_n=B_(n+1) (D) B_(n+1)-B_n=A_(n+1)

For any n in N, int_(0)^(pi) (sin (2n+1)x)/(sinx)dx is equal to

Let a_(n)=int_(0)^(pi//2)(1-sint )^(n) sin 2t, then lim_(n to oo)sum_(n=1)^(n)(a_(n))/(n) is equal to

For U_n=int_0^1x^n(2-x)^n dx ; V_n=int_0^1x^n(1-x)^ndxn in N , which of the following statement(s) is/are true? U_n=2^n V_n (b) U_n=2^(-n)V_n U_n=2^(2n)V_n (d) V_n=2^(-2n)U_n

If I_n=int_(pi/4)^(pi/2) (tanx)^-n dx(ngt1) , then I_n+I_(n+2)= (A) 1/(n-1) (B) 1/(n+1) (C) -1/(n+1) (D) 1/n-1

If sum_(r=0)^(n){a_(r)(x-alpha+2)^(r)-b_(r)(alpha-x-1)^(r)}=0 , then (a) b_(n) = 1+a_(n) (b) b_(n) = (-1)^(n)xxa_(n) (c) b_(n) = (-1)^(n-1) xxa_(n) (d) b_(n) + 1 = a_(n)

The value of int_0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >= 0 pi/2 (b) 0 (c) pi (d) 2pi

If sum_(r=1)^n r^4= a_n then sum_(r=1)^n(2r-1)^4)= (A) a_(2n)+a_n (B) a_(2n)-a_n (C) a_(2n)-16a_n (D) a_(2n)+16b_n

If n!=1, int_0^(pi/4) (tan^nx+tan^(n-2)x)d(x-[x])= (A) 1/(n-1) (B) 1/(n+1) (C) 1/n (D) 2/(n-1)

If alphaa n dbeta are the rootsof he equations x^2-a x+b=0a n dA_n=alpha^n+beta^n , then which of the following is true? a. A_(n+1)=a A_n+b A_(n-1) b. A_(n+1)=b A_(n-1)+a A_n c. A_(n+1)=a A_n-b A_(n-1) d. A_(n+1)=b A_(n-1)-a A_n

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -Level - 1
  1. about to only mathematics

    Text Solution

    |

  2. If x=int(0)^(t^(2))e^(sqrt(z)){(2tan sqrt(z)+1-tan^(2)sqrt(z))/(2sqrt(...

    Text Solution

    |

  3. IfAn=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,bn=int0^(pi/2)((sinn x)/(sinx))...

    Text Solution

    |

  4. Let u=int0^1("ln"(x+1))/(x^2+1)dxa n dv=int0^(pi/2)ln(sin2x)dx ,t h e ...

    Text Solution

    |

  5. Find Lim {x->oo}{ (1+1/(n^2))^(2/n^2)(1+4/(n^2))^(4/n^2).....(1+(n^2)/...

    Text Solution

    |

  6. The freezing point of an aqueous solution of KCN containing 0.1892" m...

    Text Solution

    |

  7. The value of underset (nrarrinfty)(lim)("sin"(pi)/(2n)."sin"(2pi)/(2n)...

    Text Solution

    |

  8. The area bounded by the curve y = cos^(-1) (cos x) and y = | x - pi| i...

    Text Solution

    |

  9. A point P moves in XY-plane in such a way that [|x|]+[|y|]=1, where [....

    Text Solution

    |

  10. If (1)/(1^(2))+(1)/(2^(2))+(1)/(3^(2))+(1)/(4^(2))+……+ oo=(pi^(2))/(6)...

    Text Solution

    |

  11. A function f(x) satisfie f(x)=f((c)/(x)) for some real number c( gt 1)...

    Text Solution

    |

  12. If 2int0^1 tan^(-1)x dx= int0^1 cot^(-1)(1-x+x^2) dx then int0^1 tan^(...

    Text Solution

    |

  13. Let f:[0,1]to R be a continuous function then the maximum value of in...

    Text Solution

    |

  14. Find the number of values of x satisfying int(0)^(x)t^(2)sin (x-t)dt=x...

    Text Solution

    |

  15. If the value of definite integral int(0)^(2)(ax +b)/((x^(2)+5x+6)^(2)...

    Text Solution

    |

  16. Let f(x) be a real valued function such that f(x)=f(121/x), AA x>0.If ...

    Text Solution

    |

  17. If the area enclosed by the curve y^(2)=4x and 16y^(2)=5(x-1)^(3) can...

    Text Solution

    |

  18. Let f(x)=x-x^(2) and g(x)=ax. If the area bounded by f(x) and g(x) is...

    Text Solution

    |

  19. Let An be the area bounded by the curve y = x^n(n>=1) and the line x=...

    Text Solution

    |

  20. If int(0)^(1)[4x^(3)-f(x)dx=(4)/(7)] then find the area of region boun...

    Text Solution

    |