Home
Class 12
MATHS
If f(x)=int(x^8+4)/(x^4-2x^2+2)dx and f(...

If `f(x)=int(x^8+4)/(x^4-2x^2+2)dx` and `f(0)=0,t h e n` (a)`f(x)` is an odd function (b)`f(x)` has range `R` (c)`f(x)` has at least one real root (d)`f(x)` is a monotonic function.

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If f(x)=int(x^(8)+4)/(x^(4)-2x^(2)+2)dx and f(0)=0, then (a) f(x) is an odd function (b) f(x) has range R(c)f(x) has at least one real root (d) f(x) is a monotonic function.

If f(x)= int_(x^2)^(x^(2) +4) e^(-t^(2) ) dt , then the function f(x) increases in

If f(2-x)=f(2+x),f(4+x)=f(4-x) and int_(0)^(2)f(x)dx=5 then int_(0)^(50)f(x)dx is

If |int_(a)^(b)f(x)dx|=int_(a)^(b)|f(x)|dx,a

Let f:(0,oo)vec R be given by f(x)=int_((1)/(x))^(x)(e^(-(t+(1)/(t)))dt)/(t), then (a)f(x) is monotonically increasing on [1,oo)(b)f(x) is monotonically decreasing on (1,oo)(b)f(x) is an odd function of x on R

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and g(x)=f'(x) is an even function , then f(x) is an odd function.

If int(x^(2)-x+1)/((x^(2)+1)^((3)/(2)))e^(x)dx=e^(x)f(x)+c, then f(x) is an even function f(x) is a bounded function the range of f(x) is (0,1)f(x) has two points of extrema

int_(-a)^(a)f(x)dx= 2int_(0)^(a)f(x)dx, if f is an even function 0, if f is an odd function.

Let f(x)= 3/(x-2)+4/(x-3)+5/(x-4) . Then f(x)=0 has (A) exactly one real root in (2,3) (B) exactly one real root in (3,4) (C) at least one real root in (2,3) (D) none of these

RESONANCE DPP-JEE MAINS-All Questions
  1. Leg pn=a^(P(n-1))-1,AAn=2,3, ,a n dl e tP1=a^x-1, where a in R^+dot ...

    Text Solution

    |

  2. If int0^x f(t)dt=x+intx^1 t f(t)dt, then f(1)= (A) 1/2 (B) 0 (C) 1 (D)...

    Text Solution

    |

  3. If f(x)=int(x^8+4)/(x^4-2x^2+2)dx and f(0)=0,t h e n (a)f(x) is an...

    Text Solution

    |

  4. The number of values of x in the interval [0,(7pi)/2] satisfying the e...

    Text Solution

    |

  5. If f(x)=int0^(pi/2)ln(1+xsin^2theta)/(sin^2theta) d theta, x >= 0 the...

    Text Solution

    |

  6. The term independent of x in the expansion of (x-1/x)^4(x+1/x)^3...

    Text Solution

    |

  7. The value of the definite integral int2^4(x(3-x)(4+x)(6-x)(10-x)+sinx...

    Text Solution

    |

  8. In any triangle A B C ,sumasin(B-C) in equal to a b+b c+c a b. 0 c...

    Text Solution

    |

  9. int0^(pi/4)((sinx+cosx)/(3+sin2x))dx

    Text Solution

    |

  10. In an equilateral triangle, the inradius and the circumradius are c...

    Text Solution

    |

  11. In a bag there are 4 Red, 3 Black, 2 Green Balls are drawn one by o...

    Text Solution

    |

  12. Find the continuous function f where (x^4-4x^2)lt=f(x)lt=(2x^2-x^3) su...

    Text Solution

    |

  13. Let J=int (-1) ^(2) (cot ^(-1) ""(1)/(x )+ cot ^(-1) x ) dx, K =int (-...

    Text Solution

    |

  14. If In=int0^(pi//4)tan^("n")x dx , prove that In+I(n-2)=1/(n+1)dot

    Text Solution

    |

  15. Twenty coupons are numbered 1,2,3......, 20 respectively. Four coup...

    Text Solution

    |

  16. If A is a square matrix of order 3, then |(A-A^T)^(105)| is equal to 1...

    Text Solution

    |

  17. The mean of the data set comprising of 16 observation is 16. If one...

    Text Solution

    |

  18. If N=2^(n-1).(2^n-1) where 2^n-1 is a prime, then the sum of the all ...

    Text Solution

    |

  19. The value of int0^(pi/4) (e^(1/(cos^2x)).sinx)/(cos^3 x)dx equals ...

    Text Solution

    |

  20. If z=sqrt(3)-2+i , then principal value of argument z is (where i=sqrt...

    Text Solution

    |