Home
Class 12
MATHS
IF M be the maximum valur of 72 int (0) ...

IF M be the maximum valur of `72 int _(0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2))dx` for `y in [0,1],` then find `M/6.

Text Solution

Verified by Experts

The correct Answer is:
4
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE AND DEFINITE INTEGRATION

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|17 Videos

  • HYPERBOLA

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-4 : Subjective Type Problems|3 Videos

  • INVERSE TRIGONOMETRIC FUNTIONS

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-5 : Subjective Type Problems|6 Videos

Similar Questions

Explore conceptually related problems

(b) int_(0)^(1)int_(y)^( sqrt(y))(x^(2)+y^(2))dydx

If x=int_(0)^(y)(dt)/(sqrt(1+9t^(2))) and (d^(2)y)/(dx^(2))=ay, then find a

int_ (0) ^ (1) (log y) / (sqrt (1-y ^ (2))) dy

int_0^1y^2sqrt(1-y^2)dy

If x=int_(0)^(y)(1)/(sqrt(1+4t^(2))) dt, then (d^(2)y)/(dx^(2)) , is

Find the maximum value of x^(m)y^(n),m,n>0 such that x+y=a.

int_(0)^(1)y dx where x=cos2y

int_0^2 int_0^sqrt(4+x^2) (dx dy)/(4+x^2+y^2) =

int_0^1 int_0^sqrt(1+x^2) (dy dx)/(1+x^2+y^2)

VIKAS GUPTA (BLACK BOOK)-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Find the value of |a| for which the area of triangle included between ...

    Text Solution

    |

  2. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

    Text Solution

    |

  3. If maximum value of int (0)^(1) (f (x ))^(2) dx under the condition -1...

    Text Solution

    |

  4. Let a differentiable function f (x) satisfies f (x). F '(-x) . F'(x) a...

    Text Solution

    |

  5. If {x} denotes the fractional part of x, then I = int (0) ^(100) (sqrt...

    Text Solution

    |

  6. Let I(n) = int (0)^(pi) (sin (n + (1)/(2))x )/(sin ((x)/(2)))dx where ...

    Text Solution

    |

  7. IF M be the maximum valur of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...

    Text Solution

    |

  8. Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...

    Text Solution

    |

  9. underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...

    Text Solution

    |

  10. The maximum value of int (-pi//2) ^(2pi//2) sin x. f (x) dx, subject t...

    Text Solution

    |

  11. Given a funtion g, continous everywhere such that g (1)=5 and int (0)^...

    Text Solution

    |

  12. If f (n)= 1/pi int (0) ^(pi//2) (sin ^(2) (n theta) d theta)/(sin ^(2)...

    Text Solution

    |

  13. Let f (2-x) =f (2+xand f (4-x )= f (4+x). Function f (x) satisfies int...

    Text Solution

    |

  14. Let l (n) =int (-1) ^(1) |x|(1+ x+ (x ^(2))/(2 ) +(x ^(2))/(3) + ........

    Text Solution

    |

  15. Let lim ( x to oo) n ^((1)/(2 )(1+(1 )/(n))). (1 ^(1) . 2 ^(2) . 3 ^(3...

    Text Solution

    |

  16. If int (a )^(b) |sin x |dx =8 and int (0)^(a+b) |cos x| dx=9 then the ...

    Text Solution

    |

  17. If f(x),g(x),h(x) and phi(x) are polynomial in x, (int1^x f(x) h(x) dx...

    Text Solution

    |

  18. If int (0)^(2)(3x ^(2) -3x +1) cos (x ^(2) -3x ^(2)+4x -2) dx = a sin ...

    Text Solution

    |

  19. let f (x) = int (0) ^(x) e ^(x-y) f'(y) dy - (x ^(2) -x+1)e ^(x) Fin...

    Text Solution

    |

  20. For a positive integer n, let I (n) =int (-pi)^(pi) ((pi)/(2) -|x|) co...

    Text Solution

    |