Home
Class 12
MATHS
(d)/(dx) int(2)^(x^(2)) (t -1) dt is equ...

`(d)/(dx) int_(2)^(x^(2)) (t -1)` dt is equal to

A

`x^(2) - 1`

B

`x(x^(2) - 1)`

C

`x-1`

D

`2x(x^(2) -1)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)/(dx)int_(2)^(x^(2)) (t -1)dt = (dt)/(dx) ((x^(2))/(2) -x^(2)) = 2x^(3) - 2x = 2x(x^(2) -1)`
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 10

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS)|50 Videos

  • PRACTICE SET 12

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos

Similar Questions

Explore conceptually related problems

(d)/(dx)(int_(f(x))^(g(x))phi(t)dt) is equal to

(d)/(dx)(int_(x^(2))^((x^(3)) (1)/(logt)dt) is equal to

(d)/(dx)(int(1)/(x^(3)(x-1))dx)=

(d)/(dx) [int_(0)^(x^(2))(dt)/(t^(2) + 4)] = ?

Let f(t)="ln"(t) . Then, (d)/(dx)(int_(x^(2))^(x^(3))f(t)" dt")

Show that (d)/(dx)int_(x^(2))^(x^(2))(1)/(log t)dt=(1)/(log x)(x^(2)-x)

Find (d)/(dx ) int _(1) ^(x ^(4)) sec t dt.

The value of the integral int_(-2012 pi)^(2012 pi){(d)/(dx)(int_(0)^(x^(2))cos t^(2)dt}dx is

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 11 -PAPER 2 (MATHEMATICS )
  1. In the Mean Value theorem (f(b)-f(a))/(b-a)=f'(c) if a=0 , b =1/2 a...

    Text Solution

    |

  2. 2x^(3) - 6x + 5 is an increasing function, if

    Text Solution

    |

  3. (d)/(dx) int(2)^(x^(2)) (t -1) dt is equal to

    Text Solution

    |

  4. int(0)^(pi//2) (cos theta)/(sqrt(4-sin^(2)theta))d theta is equal to

    Text Solution

    |

  5. int x{f(x)^(2) g''(x^(2))-f''(x^(2)) g(x^(2))}dx is equal to

    Text Solution

    |

  6. lim(x to (pi)/(6)) [(3sinx - sqrt(3)cos x)/(6x -pi)] is equal to

    Text Solution

    |

  7. Let f(x) = {{:(,x +1,"where " x lt 2),(,2x -1,"where" x ge 2):} then ...

    Text Solution

    |

  8. Show that the area' bounded by the curve y = ce^x (c> 0), the x-axis a...

    Text Solution

    |

  9. Let inputs of p and q be 1 and 0 respectively in electric circuit ...

    Text Solution

    |

  10. Digital circuit shown beow represents Boolea expression as

    Text Solution

    |

  11. If a^(2),b^(2),c^(2) are in AP, then which of the following is also an...

    Text Solution

    |

  12. Geometric mean of 7,7^(2), 7^(3) ,……….7^(n) is

    Text Solution

    |

  13. The sum of the distance of a point (2,-3) form the foci of an ell...

    Text Solution

    |

  14. A={1,2},B={{1},{2}},C={{1,2}}. Then, which of the following relation i...

    Text Solution

    |

  15. R is a relation on N given by R={(x,y):4x+3y=20}. Which of the follo...

    Text Solution

    |

  16. At what point on the curve x^(3) - 8a^(2) y= 0 the slope of the nor...

    Text Solution

    |

  17. The radius of a cylinder is increasing at the rate of 3ms^(-1) and its...

    Text Solution

    |

  18. The inverse matrix of A=[(0,1,2),(1,2,3),(3,1,1)] is

    Text Solution

    |

  19. If the x-coordinate of a point P on the jon of Q(2,2,1) and R(5,1,-2) ...

    Text Solution

    |

  20. The length of longer diagonal of the parallelogram constructed on 5...

    Text Solution

    |