Home
Class 12
MATHS
If y=int(x^(2))^(x^(3))1/(logt)dt(xgt0),...

If `y=int_(x^(2))^(x^(3))1/(logt)dt(xgt0)`, then find `(dy)/(dx)`

Text Solution

Verified by Experts

`y=int_(x^(2))^(x^(3))1/(logt)dt`
`:. (dy)/(dx)=1/(logx^(3)) d/(dx)(x^(3))-1/(logx^(2))d/(dx)(x^(2))`
`=(3x^(2))/(3logx)-(2x)/(2logx)`
`=(x^(2)-x)/(logx)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLE_TYPE|20 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CAE_TYPE|88 Videos

  • CURVE TRACING

    CENGAGE PUBLICATION|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

If y=x/(x+3) , then find dy/dx

int(x^(2)-1)/(x^(4)+3x^(2)+1)dx(xgt0) is

If y=(1-x)tan(x/2) , then find dy/dx

If y=(4x+2)(x-1) , then find dy/dx

If y=1/(1+x^3) , then find dy/dx

If y=sec^(-1)(1/(2x^2-1));0ltxlt (sqrt(2)), then find= (dy)/(dx)

If y=(1+x)(1+x^2)(1+x^4)...(1+x^(2^n)), then find (dy)/(dx)a tx=0.

If y=sin(x^2-3x) , then find dy/dx

If y=int_(0)^(x)(t-1)(t-2)^(2)dt , find x for which (dy)/(dx)=0 .

If y=(1)/(x^(4)+x^(2)+1) , then find dy/dx

CENGAGE PUBLICATION-DEFINITE INTEGRATION -JEE ADVANCED
  1. If y=int(x^(2))^(x^(3))1/(logt)dt(xgt0), then find (dy)/(dx)

    Text Solution

    |

  2. Let f be a non-negative function defined on the interval [0,1]. If int...

    Text Solution

    |

  3. The value of int0^1(x^4(1-x)^4)/(1+x^2)dxi s//a r e (22)/7-pi (b) 2/...

    Text Solution

    |

  4. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  5. The value of int(in2)^sqrt(in3) (xsinx^2)/(sinx^2+sin(In6-x^2)dx is

    Text Solution

    |

  6. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  7. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

    Text Solution

    |

  8. Let f : [0,2] rarr R be a function which is continuous on [0 , 2] and ...

    Text Solution

    |

  9. int((pi)/4)^((pi)/2)(2cosecx)^17 dx

    Text Solution

    |

  10. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

    Text Solution

    |

  11. The value of int(-pi/2)^(pi/2) (x^2cosx)/(1+e^x) dx is equal to

    Text Solution

    |

  12. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. Let S be the area of the region enclosed by y=e^(-x^(2)),y=0, x=0 and ...

    Text Solution

    |

  15. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

    Text Solution

    |

  16. Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be ...

    Text Solution

    |

  17. Let f:(0,oo)rarrRR be given by f(x)=oversetxunderset(1/x)inte^((t+1/...

    Text Solution

    |

  18. The option(s) with the values of a and L that satisfy the following eq...

    Text Solution

    |

  19. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2, pi/2). T...

    Text Solution

    |

  20. find the period of sin(x/2)-cos(x/3) is

    Text Solution

    |

  21. Let f: Rto(0,1) be a continuous function. Then, which of the following...

    Text Solution

    |