Home
Class 12
MATHS
If f(x) is integrable over [1,2], then i...

If `f(x)` is integrable over `[1,2],` then `int_1^2f(x)dx` is equal to (a) `("lim")_(ntooo)1/nsum_(r=1)^nf(r/n)` (b) `("lim")_(ntooo)1/nsum_(r=n+1)^(2n)f(r/n)` (c) `("lim")_(ntooo)1/nsum_(r=1)^nf((r+n)/n)` (d) `("lim")_(ntooo)1/nsum_(r=1)^(2n)f(r/n)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos
  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

If f(x) is integrable over [1,2] then int_(1)^(2)f(x)dx is equal to (a) lim_(nto oo) 1/n sum_(r=1)^(n)f(r/n) (b) lim_(nto oo) 1/n sum_(r=n+1)^(2n) f(r/n) (c) lim_(nto oo) 1/n sum_(r=1)^(n)f((r+n)/n) (d) lim_(nto oo) 1/n sum_(r=1)^(2n)f(r/n)

lim_(nto oo) (1)/(n^(2))sum_(r=1)^(n) re^(r//n)=

Evaluate lim_(n->oo)1/nsum_(r=n+1)^(2n)log_e(1+r/n)

lim_(n to oo) sum_(r=1)^(n) (1)/(n)e^(r//n) is

lim_(nto oo)sum_(r=1)^(n)r/(n^(2)+n+4) equals

lim_(n->oo)1/nsum_(r=1)^(2n)r/(sqrt(n^2+r^2)) equals

The value of lim_(ntooo)sum_(r=1)^(n)cot^(-1)((r^(3)-r+1/r)/2) is

If sum_(r=1)^(n) T_(r)=(n(n+1)(n+2)(n+3))/(8) , then lim_(ntooo) sum_(r=1)^(n) (1)/(T_(r))=

Evaluate lim_(ntooo) (4^(n)+5^(n))^(1//n)

The value of lim_(n to oo)sum_(r=1)^(n)(1)/(n) sqrt(((n+r)/(n-r))) is :

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. If f(2-x)=f(2+x) and f(4-x)=f(4+x) for all x and f(x) is a function fo...

    Text Solution

    |

  2. int(-1)^2|x^3-x|dxdot

    Text Solution

    |

  3. If f(x) is integrable over [1,2], then int1^2f(x)dx is equal to (a) (...

    Text Solution

    |

  4. Evaluate: int(-pi/2)^(2pi)sin^(-1)(sinx)dx

    Text Solution

    |

  5. The value of int0^(pi/4)sin2xdx is

    Text Solution

    |

  6. Let: an=int0^(pi/2)(1-sint)^nsin2tdt Then find the value of lim(n->o...

    Text Solution

    |

  7. Q. int0^pie^(cos^2x)( cos^3(2n+1) x dx, n in I

    Text Solution

    |

  8. Prove that int0^(102)(x-1)(x-2)..(x-100)xx(1/(x-1)+1/(x-2)+.... .+ 1/...

    Text Solution

    |

  9. Let f:[0,2]->R be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  10. Evaluate: int0^1(1)/((1+x^2)sqrt(1-x^2))dx

    Text Solution

    |

  11. If f(x)={(e^cosx sinx ,, |x| leq 2),(2 ,, other wise):}. Then int-2^...

    Text Solution

    |

  12. Evaluate: int0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx

    Text Solution

    |

  13. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx= pi^2

    Text Solution

    |

  14. Prove that 1 lt underset(0)overset(2)int((5-x)/(9-x^(2)))dx lt 6/5

    Text Solution

    |

  15. If the difference between the roots of the equation x^2+""a x""+""1...

    Text Solution

    |

  16. If m is the least value (global minimum) and M is the greatest value (...

    Text Solution

    |

  17. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

    Text Solution

    |

  18. Show that inta^b(|x|)/x dx=|b|-|a|dot

    Text Solution

    |

  19. The value of (pi^2)/(1n3)int(7/6)^(5/6)sec(pix)dxi s

    Text Solution

    |

  20. Let: f(x)=int0^x|2t-3|dtdot Then discuss continuity and differentiabil...

    Text Solution

    |