Home
Class 12
MATHS
If f(x) and g(x) are continuous function...

If `f(x)` and `g(x)` are continuous functions, then `int_(In lamda)^(In (1//lamda))(f(x^(2)//4)[f(x)-f(-x)])/(g(x^(2)//4)[g(x)+g(-x)])dx` is

A

depend on `lambda`

B

a non-zero constant

C

zero

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 1 Part-III|2 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 2 Part - 1|30 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 1|31 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

  • DPP

    RESONANCE|Exercise QUESTION|665 Videos

Similar Questions

Explore conceptually related problems

int_(ln lambda)^(ln (1/lambda)) (f(x^2/3)(f(x)+f(-x)))/(g(3x^2)(g(x)-g(-x))) dx=

If f(x) and g(x) are two continuous functions defined on [-a,a], then the value of int_(-a)^(a){f(x)+f(-x)}{g(x)-g(-x)}dx is

int(f(x)g'(x)+g(x)f'(x))/(f(x)g(x))[logf(x)+logg(x)]dx=

Let f:R rarr R and g:R rarr R be continuous functions.Then the value of the integral int_((pi)/(2))^((pi)/(2))[f(x)+f(-x)][g(x)-g(-x)]dx is

int x{f(x^(2))g'(x^(2))-f'(x^(2))g(x^(2))}dx

If f(x) and g(x) are continuous functions satisfying f(x) = f(a-x) and g(x) + g(a-x) = 2 , then what is int_(0)^(a) f(x) g(x)dx equal to ?

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 1 Part-II
  1. int(0)^(oo)(x^(2)+1)/(x^(4)+7x^(2)+1)dx=

    Text Solution

    |

  2. Suppose for every integer n, .int(n)^(n+1) f(x)dx = n^(2). The value o...

    Text Solution

    |

  3. If f(x) and g(x) are continuous functions, then int(In lamda)^(In (1//...

    Text Solution

    |

  4. int- 1^1cot^(- 1)((x+x^3)/(1+x^4))dx

    Text Solution

    |

  5. int(2)^(0){x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)} dx is equal to

    Text Solution

    |

  6. int(-1)^(1)xln(1+e^(x))dx=

    Text Solution

    |

  7. If int(-1)^(3//2)|xsinpix|dx = (k)/(pi^(2)), then the value of k is :

    Text Solution

    |

  8. The value of definite integral int0^(pi^2/4) dx/(1+sin^2 sqrtx+ cos^2 ...

    Text Solution

    |

  9. int(2-ln3)^(3+ln3)(ln(4+x))/(ln(4+x)+ln(9-x))dx is equal to :

    Text Solution

    |

  10. The value of the definite integral l = int(0)^(x)xsqrt(1+|cosx|) dx is...

    Text Solution

    |

  11. The value of int(0)^(pi//2)ln|tanx+cotx| dx is equal to :

    Text Solution

    |

  12. If I1=int0^1(e^x)/(1+x) dxaand I2=int0^1 x^2/(e^(x^3)(2-x^3)) dx then ...

    Text Solution

    |

  13. The value of int(0)^(|x|){x} dx (where [*] and {*} denotes greatest in...

    Text Solution

    |

  14. If int(0)^(11) (11^(x))/(11^([x]))dx = k/(log11), (where [] denotes gr...

    Text Solution

    |

  15. f(x) = int(x)^(x^(2))(e^(t))/(t)dt, then f'(t) is equal to :

    Text Solution

    |

  16. f(x) = underset(0)overset(x)(t-1)(t-2)^(2)(t-4)^(5) dt (xgt0) then num...

    Text Solution

    |

  17. Lim(hto0)(int(a)^(x+h)ln^(2)tdt-inta^(x)ln^(2)tdt)/(h) equals to :

    Text Solution

    |

  18. The value of the function f(x) = 1+x+int(1)^(x)(ln^(2)t+2lnt)dt, where...

    Text Solution

    |

  19. If int(a)^(y)cost^(2)dt = int(a)^(x^(2))(sint)/(t) dt, then the value ...

    Text Solution

    |

  20. If int(sinx)^(1)t^(2) (f(t)) dt = (1-sinx), then f ((1)/(sqrt(3))) is

    Text Solution

    |