Home
Class 12
MATHS
For Un=int0^1x^n(2-x)^n dx ; Vn=int0^1x...

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? (a)`U_n=2^n V_n` (b) `U_n=2^(-n)V_n` (c)`U_n=2^(2n)V_n` (d) `V_n=2^(-2n)U_n`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    RESONANCE DPP|Exercise All Questions|9 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

Similar Questions

Explore conceptually related problems

U_(n)=int_(0)^(1)x^(n)(2-x)^(n)dx and V_(n)=int_(0)^(1)x^(n)(1-x)^(n)dx,n in N and if (V_(n))/(U_(n))=1024, then the value of n is

int_(n)^(n+1)f(x)dx=n^(2)+n then int_(-1)^(1)f(x)dx=

Prove that: I_(n)=int_(0)^(oo)x^(2n+1)e^(-x^(2))dx=(n!)/(2),n in N

Find sum_(n=1)^n u_n if u_n=sum_(n=0)^n1/2^n .

If u _(n) = int _(0) ^(pi//2) x ^(n) sin x dx, n in N then the value of u _(10) + 90 u _(s) is

If u_(n)=int(log x)^(n)dx, then u_(n)+nu_(n-1) is equal to :

If I_(n)=int_(0)^(1)(dx)/((1+x^(2))^(n));n in N, then prove that 2nI_(n+1)=2^(-n)+(2n-1)I_(n)

A_(n)=int_(0)^((pi)/(2))(sin(2n-1)x)/(sin x)dx;B_(n)=int_(0)^((pi)/(2))((sin nx)/(sin x))^(2)dx; for n in N then A_(n+1)=A_(n)( b) B_(n+1)=B_(n)A_(n+1)-A_(n)=B_(n+1)(d)B_(n+1)-B=A_(n+1)

RESONANCE DPP-INTEGRALS-All Questions
  1. int(x^6+1)/(x^2+1)dxi se q u a l (x^5)/5+(x^3)/3+x+c (b) (x^5)/5-(x^...

    Text Solution

    |

  2. If In=intsin^n xdx ; n in N , then 5I4-6I6 is equal to 1.sinx(co...

    Text Solution

    |

  3. If Im=int1^e (lnx)^m dx ,m in N , then I(10)+10 I9 is equal to (A) ...

    Text Solution

    |

  4. int(xdx)/(sqrt((1+x^2)+sqrt((1+x^2)^3)))= (a) 1/2ln(1+sqrt(1+x^2))+...

    Text Solution

    |

  5. The value of int(-2pi)^(5pi)cot^(-1)(tanx)dxi se q u a lto (7pi)/2 (...

    Text Solution

    |

  6. int((1+(log)e x)^2)/(1+(log)e x^(x+1)+((log)e x^(sqrt(x)))^2)dx=

    Text Solution

    |

  7. intsqrt(1+2cotx(cotx+cos e cx))dx is equal to (A) 2I n(cos x/2)+c (B...

    Text Solution

    |

  8. int0^pisin^3theta(1+2costheta)(1+costheta)^2 d theta is equal to (a...

    Text Solution

    |

  9. For Un=int0^1x^n(2-x)^n dx ; Vn=int0^1x^n(1-x)^ndxn in N , which ...

    Text Solution

    |

  10. Evaluate int(x+2)/((x^2+3x+3)sqrt(x+1))dx

    Text Solution

    |

  11. int(cos^3x)/(sqrt(sin^7x))dx= 2/5dotcos e c^(7/2)x+2sqrt(cose c x)+c...

    Text Solution

    |

  12. int0^9{sqrt(x)}dx , where {x} denotes the fractional part of x , is 5 ...

    Text Solution

    |

  13. The value of int(-(pi/4)^(1/3))^((pi/4)^(1/3))(x^2)/((1+sin^2x^3)(1+e...

    Text Solution

    |

  14. If int0^1tan^(-1)xdx=alpha,t h e nint0^(pi/4)tan^(-1)((2cos^2theta)/(...

    Text Solution

    |

  15. If f is a function with period P, then inta^(a+p)f(x)dx is equal to...

    Text Solution

    |

  16. The value of int1^(e^(37))(pisin(piI nx))/xdx is 2 (b) 4 (c) e^(27)...

    Text Solution

    |

  17. If int((x^(-7/6)-x^(5/6)))/(x^(1/3)(x^2+x+1)^(1/2)-x^(1/2)(x^2+x+1)^(...

    Text Solution

    |

  18. int(-1)^1(x^3|x|+1)/(x^2+2|x|+1)dx=aln2+bt h e n a=2; b=1 (b) a=2; b...

    Text Solution

    |

  19. int((x/e)^x+(e/x)^x)I nxdx= (a)(e/x)^x-(x/e)^x+c (b) (x/e)^x+(e/x...

    Text Solution

    |

  20. Let A=int0^1(e^t)/(t+1)dt , then the value of (int0^1t e^t^2)/(t^2+1)...

    Text Solution

    |