Home
Class 12
MATHS
int (0)^(a) (xdx)/(sqrt(a^(2)+x^(2)) ) ...

` int _(0)^(a) (xdx)/(sqrt(a^(2)+x^(2)) )` is equal to

A

`a(sqrt2-1)`

B

`a(1-sqrt2)`

C

`a(1+sqrt2)`

D

`2asqrt3`

Text Solution

Verified by Experts

The correct Answer is:
A
Put ` t = a^(2) +x^(2) rArr 2xdx = dt`
` :. int _(0)^(a) (xdx)/(sqrt(a^(2)+x^(2)) )= 1/2 int _(a^(2))^(2a^(2)) 1/(sqrt(t)) dt `
` = [ ( 2a^(2) )^(1/2) - a^(2/2)]= a (sqrt(2)-1)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)|76 Videos

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • DIFFERENTIAL EQUATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|27 Videos

Similar Questions

Explore conceptually related problems

The value of int_(0)^(a)(dx)/(x+sqrt((a^(2)-x^(2))) is equal to

int _(0)^(a) sqrt(a^(2) - x^(2)) dx is equal to

*1. int(xdx)/(sqrt(a^(2)+x^(2)))

int(xdx)/(sqrt(x^(2)-a^(2)))=

(b) int(xdx)/(sqrt(1-x^(2)))

The value of int_(0)^(oo)(xdx)/((1+x)(1+x^(2))) is equal to

int(xdx)/(sqrt(1-2x^(4)))=

" (2) "int(xdx)/(sqrt(x^(2)-1))

" (1) "int(xdx)/(sqrt(1+x^(2)))

3.(i) int(xdx)/((sqrt(x^(2)+2))

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
  1. int (0)^(a) (xdx)/(sqrt(a^(2)+x^(2)) ) is equal to

    Text Solution

    |

  2. int (-pi/2)^(pi/2)log((2-sin x)/(2+sinx))dx is equal to

    Text Solution

    |

  3. int (0)^(pi //2)((root(n)(secx))/(root(n)(secx)+root(n)("cosec"x)))dx=

    Text Solution

    |

  4. The value of int 0 ^ 1 x ^ 2 ( 1 - x ^ 2 ) ^ (3//2 ) dx ...

    Text Solution

    |

  5. The value of int0^oox/((1+x)(x^2+1))dx is

    Text Solution

    |

  6. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

    Text Solution

    |

  7. int(pi//2)^(pi//2)(cosx)/(1+e^(x))dx is equal to

    Text Solution

    |

  8. int(0)^(pi//2)(1)/((1+tanx))dx=?

    Text Solution

    |

  9. If int(0)^(1) tan^(-1) x dx = p , then the value of int(0)^(1) tan^(-1...

    Text Solution

    |

  10. The value of int (0)^(pi//2) log ("cosec "x) dx is

    Text Solution

    |

  11. Which of the following is true ?

    Text Solution

    |

  12. int(0)^(5) 1/((x-1)(x-2))dx is equal to

    Text Solution

    |

  13. int(pi/4)^(pi/2) e^x(logsinx+cotx)dx

    Text Solution

    |

  14. The value of int(0)^(pi) x sin^(3) x dx is

    Text Solution

    |

  15. The value of int0 ^(pi/2) (cos3x+1)/(cosx - 1) dx is equal to

    Text Solution

    |

  16. The value of underset(0)overset(1)int tan^(-1) ((2x-1)/(1+x-x^(2)))dx ...

    Text Solution

    |

  17. If f is a continous function, then

    Text Solution

    |

  18. The value of int(-pi)^(pi) sin^(3) x cos^(2) x dx is equal to

    Text Solution

    |

  19. The value of int(-1)^(1) log ((x-1)/(x+1))dx is

    Text Solution

    |

  20. int(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx=(pi)/(12)

    Text Solution

    |

  21. int (1)^(2)e^(x) (1/x - 1/(x^(2)))dx is qual to

    Text Solution

    |