Home
Class 12
MATHS
int(dx)/((1+sqrtx)^(2010))=2[(1)/(alpha(...

`int(dx)/((1+sqrtx)^(2010))=2[(1)/(alpha(1+sqrtx)^(alpha))-(1)/(beta(1+sqrtx))^(beta)]+c` where `alpha, betagt0" then "alpha-beta` is

A

1

B

2

C

`-1`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
A
`int(dx)/((1+sqrtx)^(2010))`
`=int(sqrtx)/(sqrtx(1+sqrtx)^(2010))dx`
`=2int(t-1)/((t-1)(t^(2010)))dt(t=1+sqrtx)`
`=2[(1)/(2009t^(2009))-(1)/(2008t^(2008))]+c`
`rArr" "alpha=2009, beta=2008`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Subjective Type|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Comprehension Type|2 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|1 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

alpha beta x ^(alpha-1) e^(-beta x ^(alpha))

If alpha+ beta=-7 and alpha beta=10 then find the value of alpha-beta=__ .

sin alpha+sinbeta=(1)/(4) and cos alpha+cos beta=(1)/(3) the value of sin(alpha+beta)

If 2alpha= -1-isqrt(3)" and"2beta= -1+isqrt(3) , then 5alpha^(4)+5beta^(4)+7alpha^(-1)beta^(-1) is equal to

If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)1+f(2)1+f(3)1+f(2)1+f(3)1+f(4)|=K(1-alpha)^2(1-beta)^2(alpha-beta)^2 , then K is equal to (1) alphabeta (2) 1/(alphabeta) (3) 1 (4) -1

If alphaa n dbeta are roots of the equation a x^2+b x+c=0, then the roots of the equation a(2x+1)^2-b(2x+1)(x-3)+c(x-3)^2=0 are a. (2alpha+1)/(alpha-3),(2beta+1)/(beta-3) b. (3alpha+1)/(alpha-2),(3beta+1)/(beta-2) c. (2alpha-1)/(alpha-2),(2beta+1)/(beta-2) d. none of these

If cos alpha + cos beta =0 = sin alpha + sin beta , then cos 2 alpha + cos 2 beta is equal to

If lim_(xrarroo) xlog_(e)(|(alpha//x,1,gamma),(0,1//x,beta),(1,0,1//x)|)=-5. then where alpha,beta,gamma are finite real numbers, then a) alpha=2,beta=1,gamma in R b) alpha=2,beta=2,gamma=5 c) alpha in R , beta=1 , gamma in R d) alpha in R , beta=1,gamma=5

CENGAGE-INDEFINITE INTEGRATION-Single Correct Answer Type
  1. The integral intsqrt(cotx)e^(sqrt(sinx))sqrt(cosx)dx equals

    Text Solution

    |

  2. int(dx)/(xsqrt(x^(6)+1)) equals

    Text Solution

    |

  3. int(dx)/((1+sqrtx)^(2010))=2[(1)/(alpha(1+sqrtx)^(alpha))-(1)/(beta(1+...

    Text Solution

    |

  4. int(sin((pi)/(4)-x)dx)/(2+sin2x)=A tan^(-1)(f(x))+B, where A, B are co...

    Text Solution

    |

  5. If sqrt(x+sqrt(x^(2)+x))dx=A{x+sqrt(x^(2)+2)}^(3//2)+(B)/(sqrt(x+sqrt(...

    Text Solution

    |

  6. int(x^(2)+1)/(xsqrt(x^(2)+2x-1)sqrt(1-x^(2)-x))dx is equal to

    Text Solution

    |

  7. int(dx)/(x^(2)sqrt(16-x^(2))) has the value equal to

    Text Solution

    |

  8. If int(3tan(x-(pi)/(4)))/(cos^(2)xsqrt(tan^(3)x)+tan^(2)x+tanx)=Ktan^(...

    Text Solution

    |

  9. int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

    Text Solution

    |

  10. int(3x^(2)+2x)/(x^(6)+2x^(5)+x^(4)+2x^(3)+2x^(2)+5)dx=

    Text Solution

    |

  11. int(1)/((1+sqrtx)sqrt(x-x^(2)))dx is equal to

    Text Solution

    |

  12. If f(x) = int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx, (x ge 0), and f...

    Text Solution

    |

  13. If I=int(dx)/(x^(4)sqrt(a^(2)+x^(2))), then I equals

    Text Solution

    |

  14. If I=intx^(27)(6x^(2)+5x+4)(x^(2)+x+1)^(6)dx=f(x)+C, then f(x) is eq...

    Text Solution

    |

  15. int(x^(2)(1-logx))/((logx)^(4)-x^(4))dx equals

    Text Solution

    |

  16. If int(x(x-1))/((x^(2)+1)(x+1)sqrt(x^(3)+x^(2)+x))dx =(1)/(2)log(e)...

    Text Solution

    |

  17. int(dx^(3))/(x^(3)(x^(n)+1)) equals

    Text Solution

    |

  18. int((x+1)^(2)x)/(x(x^(2)+1)) is equal to

    Text Solution

    |

  19. int(x^3-x)/(1+x^6)dx is equal to

    Text Solution

    |

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

    Text Solution

    |