Home
Class 12
MATHS
Let f(x)=int0^xe^t(t-1)(t-2)dt, Then f d...

Let `f(x)=int_0^xe^t(t-1)(t-2)dt`, Then f decreases in the interval

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = int_2^x f(t^2-3t+2) dt then

If f(x)=int_(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.

If f(x)=int_0^x(sint)/t dt ,x >0, then

Let f(x) be a differentiable function satisfying f(x)=int_(0)^(x)e^((2tx-t^(2)))cos(x-t)dt , then find the value of f''(0) .

If f(x)=int_(x^(2))^(x^(2)+1)e^(-t^(2))dt , then the interval in which f(x) is increasing, is-

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

Let f(x)=1/x^2 int_4^x (4t^2-2f'(t))dt then find the value of 9f'(4)

f(x)=int_1^x(tan^(-1)(t))/t dt \ AAx in R^+, then find the value of f(e^2)-f(1/(e^2))

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Prove that for any two numbers x1 and x2.(2e^(x1)+e^(x2))/3gte^((2(x1)...

    Text Solution

    |

  2. Assertion Consider the following statements in SandR S: Both sinx and...

    Text Solution

    |

  3. Let f(x)=int0^xe^t(t-1)(t-2)dt, Then f decreases in the interval

    Text Solution

    |

  4. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  5. Tangent is drawn to ellipse (x^2)/(27)+y^2=1 at (3sqrt(3)costheta,sint...

    Text Solution

    |

  6. If f(x)=xe^(x(1-x)) , then f(x) is(a) increasing on [−1/2,1] (b) decr...

    Text Solution

    |

  7. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x) as b...

    Text Solution

    |

  8. Suppose that f is a polynomial of degree 3 and that f^(x)!=0 at any...

    Text Solution

    |

  9. The maximum value of the function f(x)=((1+x)^(0. 6))/(1+x^(0. 6)) in ...

    Text Solution

    |

  10. The value of a for which the functionf(x)=asinx+1/3sin3x has an extrem...

    Text Solution

    |

  11. If f(x)=(t+3x-x^2)/(x-4), where t is a parameter that has minimum and ...

    Text Solution

    |

  12. A factory D is to be connected by a road with a straight railway line ...

    Text Solution

    |

  13. Let f(x)=ax^3+bx^2+cx+1 has exterma at x=alpha,beta such that alpha ...

    Text Solution

    |

  14. Consider the function f(x)=xcosx-sinxdot Then identify the statement w...

    Text Solution

    |

  15. The number of values of k for which the equation x^3-3x+k=0 has two di...

    Text Solution

    |

  16. The least natural number a for which x+a x^(-2)>2AAx in (0,oo) is 1 (b...

    Text Solution

    |

  17. A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local max...

    Text Solution

    |

  18. A rectangle of the greatest area is inscribed in a trapezium A B C D ,...

    Text Solution

    |

  19. f(x)={4x-x^3+ln(a^2-3a+3),0lt=x<3 x-18 ,xgeq3 complete set of values...

    Text Solution

    |

  20. Let the function f(x) be defined as follows:(x)= {x^3 +x^2 −10x,−1≤x<...

    Text Solution

    |