Home
Class 12
MATHS
int(0)^((alpha)/3)(f(x))/(f(x)+f((alpha-...

`int_(0)^((alpha)/3)(f(x))/(f(x)+f((alpha-3x)/3))dx=`

A

`(2alpha)/3`

B

`(alpha)/2`

C

`(alpha)/3`

D

`(alpha)/6`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise EVALUATIO TEST|30 Videos
  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise CRITICAL THINKING|115 Videos
  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 Videos
  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(a)(f(x))/(f(x)+f(a-x))dx=

Let int_(alpha)^( beta)(f(alpha+beta-x))/(f(x)+f(alpha+beta-x))dx=4 then

int_(0)^(a) (f(a+x) + f(a-x) ) dx =

int_(0)^(a)[f(x)+f(a-x)]dx=

P(alpha,f(alpha)) and Q(beta,f(beta)) are ends of an arc in the first quadrant.The area bounded by the arc,ordinates through P and Q, and the x -axis is (A) int_(f(alpha))^(f(beta))f^(-1)(y)dy(B)int_(alpha)^( beta)f^(-1)(y)dy(C)int_(alpha)^( beta)f(x)dx(D)int_(f(alpha))^(f(beta))f(x)dx

Let a function f(x,alpha) be continuous for a<=x<=b and 0<=a<=d. Then,for any alpha in[c,d], if I(alpha)=int_(a)^(b)f(x,alpha)dx, then (d)/(d alpha)(I(alpha))=int_(a)^(b)rho(f(x,alpha))/(rho alpha)dx

Let g(x)=|(f(x+alpha), f(x+2a), f(x+3alpha)), f(alpha), f(2alpha), f(3alpha),(f\'(alpha),(f\'(2alpha), f\'(3alpha))| , where alpha is a constant then Lt_(xrarr0(g(x))/x= (A) 0 (B) 1 (C) -1 (D) none of these

int_(2)^(3)f(5-x)dx-int_(2)^(3)f(x)dx=

Let f(x)=(e^(x)+1)/(e^(-x)-1) and int_(0)^(1)x^(3)(e^(x)+1)/(e^(x)-1) dx=alpha"then", int_(-1)^(1)int t^(3)f(t)dt is equal to

TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
  1. If int(0)^((pi)/2)log(cosx)dx=-(pi)/2log2, then int(0)^((pi)/2)log(cos...

    Text Solution

    |

  2. int(0)^(pi//2) sin 2x log (tan x) dx is equal to

    Text Solution

    |

  3. int(0)^((alpha)/3)(f(x))/(f(x)+f((alpha-3x)/3))dx=

    Text Solution

    |

  4. Let f be a non constant continuous function for all xge0. Let f satisf...

    Text Solution

    |

  5. int(0)^(pi)(xdx)/(1+sinx) is equal to

    Text Solution

    |

  6. int(0)^(pi)(x dx)/(4 cos^(2)x+9sin^(2)x)=

    Text Solution

    |

  7. int0^pi(ntanx)/(secx+cosx)dx

    Text Solution

    |

  8. int0^(pi/2) (xsinxcosx)/(cos^4x+sin^4x) dx=

    Text Solution

    |

  9. int0^1log(1+x)/(1+x^2)dx

    Text Solution

    |

  10. The value of int(8 log(1+x))/(1+x^(2)) dx is

    Text Solution

    |

  11. int(0)^(pi)[cotx]dx, where [.] denotes the greatest integer function, ...

    Text Solution

    |

  12. int2^8 sqrt(10-x)/(sqrtx+sqrt(10-x))dx

    Text Solution

    |

  13. int(2016)^(2017)(sqrt(x))/(sqrt(x)+sqrt(4033-x))dx is equal to

    Text Solution

    |

  14. int(pi//4)^(3pi//4)(dx)/(1+cosx) is equal to

    Text Solution

    |

  15. The integral int2^4(logx^2)/(logx^2+log(36-12 x+x^2)dx is equal to:...

    Text Solution

    |

  16. The value of int(-pi//2)^(pi//2)(1)/(e^(sinx)+1) dx is equal to

    Text Solution

    |

  17. The value of overset(sqrt("In"3))underset(sqrt("In"2))int(xsinx^(2))/(...

    Text Solution

    |

  18. The value of the integral I = int(1//2014)^(2014)(tan^(-1) x)/x dx is

    Text Solution

    |

  19. The value of the definite integral 1/pi int(pi/2)^((5pi)/2) e^(tan^(-...

    Text Solution

    |

  20. If f(x)=f(pi+e-x) and inte^pif(x)dx=2/(e+pi), then inte^pi xf(x)dx is ...

    Text Solution

    |