Home
Class 12
MATHS
If y = underset(u(x))overset(v(x))intf(t...

If `y = underset(u(x))overset(v(x))intf(t) dt`, let us define `(dy)/(dx)` in a different manner as `(dy)/(dx) = v'(x) f^(2)(v(x)) - u'(x) f^(2)(u(x))` alnd the equation of the tangent at `(a,b)` as `y -b = (dy/dx)_((a,b)) (x-a)`
If `F(x) = underset(1)overset(x)inte^(t^(2)//2)(1-t^(2))dt`, then `d/(dx) F(x)` at `x = 1` is

A

`x+y=1`

B

`y=x-1`

C

`y=x`

D

`y=x+1`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|4 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|5 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|10 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

If y =int _(u(x))^(v(x))f(t) dt , let us define (dy)/(dx) in a different manner as (dy)/(dx) = v'(x) f^(2)(v(x)) - u'(x) f^(2)(u(x)) alnd the equation of the tangent at (a,b) as y -b = (dy/dx)_((a,b)) (x-a) If F(x) = int_(1)^(x)e^(t^(2)//2)(1-t^(2))dt , then d/(dx) F(x) at x = 1 is

If y = int_(u(x))^(v(x))f(t) dt , let us define (dy)/(dx) in a different manner as (dy)/(dx) = v'(x) f^(2)(v(x)) - u'(x) f^(2)(u(x)) alnd the equation of the tangent at (a,b) as y -b = (dy/dx)_("(a,b)") (x-a) If y = int_(x)^(x^(2)) t^(2)dt , then equation of tangent at x = 1 is

If y = int_(u(x))^(v(x))f(t) dt , let us define (dy)/(dx) in a different manner as (dy)/(dx) = v'(x) f^(2)(v(x)) - u'(x) f^(2)(u(x)) alnd the equation of the tangent at (a,b) as y -b = (dy/dx)_((a,b)) (x-a) if int_(x^(3))^(x^(4))lnt dt , then lim_(xrarr0^(+)) (dy)/(dx) is

Let f'(x)=sin(x^(2)) and y=f(x^(2)+1) then (dy)/(dx) at x=1 is

Differentiate f(x) = (x+2)^(2/3) (1-x)^(1/3) w.r.t. x

Theorem: (d)/(dx)(int f(x)dx=f(x)

If (d(f(x))/(dx)=(1)/(1+x^(2)) then (d)/(dx){f(x^(3))} is

Let y=f(x) satisfy the differential equation (dy)/(dx)=(x+y)/(x),y(1)=1, then y((1)/(e)) is equal

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Passage Based Questions)
  1. Suppose lim(xrarr0) (int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- si...

    Text Solution

    |

  2. Suppose lim(xrarr0)(int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sinx...

    Text Solution

    |

  3. Suppose sum(x to 0)(int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sin...

    Text Solution

    |

  4. Suppose f(x) and g(x) are two continuous functions defined for 0<=x<...

    Text Solution

    |

  5. Suppose f(x) and g(x) are two continuous functions defined for 0<=x<...

    Text Solution

    |

  6. Suppose f(x) and g(x) are two continuous functions defined for 0<=x<...

    Text Solution

    |

  7. We are given the curvers y=int(- infty)^(x) f(t) dt through the point ...

    Text Solution

    |

  8. We are given the curves y=int(-oo)^(x)f(t) dt through the point (0,(...

    Text Solution

    |

  9. We are given the curvers y=int(- infty)^(x) f(t) dt through the point ...

    Text Solution

    |

  10. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

    Text Solution

    |

  11. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

    Text Solution

    |

  12. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

    Text Solution

    |

  13. If y = underset(u(x))overset(v(x))intf(t) dt, let us define (dy)/(dx) ...

    Text Solution

    |

  14. Let y= int(u(x))^(y(x)) f (t) dt, let us define (dy)/(dx) as (dy)/(dx)...

    Text Solution

    |

  15. If y = underset(u(x))overset(v(x))intf(t) dt, let us define (dy)/(dx) ...

    Text Solution

    |

  16. Consider f:(0, oo)->(-pi/2,pi/2), defined as f(x) = tan^-1 (loge x/(...

    Text Solution

    |

  17. The value of int(0)^(infty)[tan^(-1)x] dx is equal to (where ,[.] deno...

    Text Solution

    |