Home
Class 12
MATHS
The absolute value of int(10)^(19) (cos...

The absolute value of `int_(10)^(19) (cosx)/(1+x^(8))dx`, is

A

less than `10^(-7)`

B

more than `10^(-7)`

C

less than `10^(-8)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
For `x gt10`, we have
`|cosx|lt1 and 1 +x^(8)gt10^(8)rArr (1)/(1+x^(8))le10^(-8)`
`:. |underset(10)overset(19)int(cos x dx)/(1+x^(8))|leunderset(10)overset(19)int(|cosx|)/(1+x^(8))dxleunderset(10)overset(19)int10^(-8)=9xx10^(-8)lt10^(-7)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|12 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|143 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 2|56 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

The value of int_(0)^(1)(8log(1+x))/(1+x^(2))dx is

Estimate the absolute value of the integral int_(10)^(19)(sinx)/(1+x^8)dx

The value of int_0^1 (x^(3))/(1+x^(8))dx is

The value of I=int_(0)^(pi//2) (1)/(1+cosx)dx is

Value of int_(1)^(9)(x-2)(x-4)(x-6)(x-8)(x-5)dx is

The value of int_(-pi)^(pi)(sqrt2cosx)/(1+e^(x))dx is equal to

The value of int_(-pi)^(pi) sinx f(cosx)dx is

The value of the integral int_(0)^(pi) (1)/(e^(cosx)+1)dx , is

The value of int_(0)^(pi)(|x|sin^(2)x)/(1+2|cosx|sinx)dx is equal to

The minimum odd value of 'a' (agt1) for which int_(10)^(19)(sinx)/(1+x^(a))dxlt(1)/(9), is equal to

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Section I - Solved Mcqs
  1. If I(1)=int(x)^(1)(1)/(1+t^(2)) dt and I(2)=int(1)^(1//x)(1)/(1+t^(2))...

    Text Solution

    |

  2. The value of int(1/e->tanx) (tdt)/(1+t^2) + int(1/e->cotx) (dt)/(t*(1+...

    Text Solution

    |

  3. The absolute value of int(10)^(19) (cosx)/(1+x^(8))dx, is

    Text Solution

    |

  4. If f(x) is an odd pefiodc function defined on the interval [T/2,T/2], ...

    Text Solution

    |

  5. If int(pi//2)^(theta) sin x dx=sin 2 theta then the of theta satisfyin...

    Text Solution

    |

  6. If f(x) is periodic function with period, T, then

    Text Solution

    |

  7. The value of lim(n rarr infty) (1)/(n) {(n+1)(n+2)(n+3)…(n+n)}^(1//n)...

    Text Solution

    |

  8. The points of extremum of phi (x)=int(1)^(x)e^(-t^(2//2)) (1-t^(2)) dt...

    Text Solution

    |

  9. int(-2)^(2) min(x-[x],-x-[x])dx equals, where [x] represents greates i...

    Text Solution

    |

  10. The integral int(0)^(a) (g(x))/(f(x)+f(a-x))dx vanishes, if

    Text Solution

    |

  11. If (1)/(sqrt(a))int(1)^(a)((3)/(2)sqrt(x)+1-(1)/(sqrt(x)))dx lt4 then ...

    Text Solution

    |

  12. Evaluate (int(0)^(n)[x]dx)/(int(0)^(n){x}dx) (where [x] and {x} are in...

    Text Solution

    |

  13. If f(x)=min{|x-1|,|x|,|x+1|, then the value of int(-1)^(1) f(x) dx is ...

    Text Solution

    |

  14. The value of int(0)^(100)[ tan ^(-1)x] d x is equal to (where [.] den...

    Text Solution

    |

  15. The value of int(-1)^(10) sgn (x-[x])dx is equal to (where, [.] denote...

    Text Solution

    |

  16. If n in N, then int(-n)^(n)(-1)^([x]) dx equals

    Text Solution

    |

  17. The value of :.int(0)^([x]) (2^(x))/(2^([x]))dx is

    Text Solution

    |

  18. If f(x) is a function satisfying f((1)/(x))+x^(2)f(x)=0 for all non ...

    Text Solution

    |

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

    Text Solution

    |

  20. The value of the integral int (e ^(-1))^(e ^(2))|(ln x )/(x)|dx is:

    Text Solution

    |